本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。

The combination of two or more portfolio rules is theoretically convex in return-risk space, which provides for a new class of portfolio rules that gives purpose to the Mean-Variance framework out-of-sample. The author investigates the performance loss from estimation risk between the unconstrained Mean-Variance portfolio and the out-of-sample Global Minimum Variance portfolio. A new two-fund rule is developed in a specific class of combined rules, between the equally weighted portfolio and a mean-variance portfolio with the covariance matrix being estimated by linear shrinkage. The study shows that this rule performs well out-of-sample when covariance estimation error and bias are balanced. The rule is performing at least as good as its peer group in this class of combined rules.

This dissertation studies three classes of estimators for the asymptotic variance parameter of a stationary stochastic process. All estimators are based on the concept of data "re-use" and all transform the output process into functions of an approximate Brownian motion process. The first class of estimators consists folded standardized time series area and Cramér-von Mises (CvM) estimators. Detailed expressions are obtained for their expectation at folding levels 0 and 1; those expressions explain the puzzling increase in small-sample bias as the folding level increases. In addition, we use batching and linear combinations of estimators from different levels to produce estimators with significantly smaller variance. Finally, we obtain very accurate approximations of the limiting distributions of batched folded estimators. These approximations are used to compute confidence intervals for the mean and variance parameter of the underlying stochastic process. The second class --- folded overlapping area estimators --- are computed by averaging folded versions of the standardized time series corresponding to overlapping batches. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity. We obtain statistical properties of these estimators such as bias and variance. Further, we find approximate confidence intervals for the mean and variance parameter of the process by approximating the theoretical distributions of the proposed estimators. In addition, we develop algorithms to compute these estimators with only order-of-sample-size work. The third class --- reflected area and CvM estimators --- are computed from reflections of the original sample path. We obtain the expected values and variance of individual estimators. We show that it is possible to obtain linear combinations of reflected estimators with smaller variance than the variance of each constituent estimator, often at no cost in bias. A quadratic optimization problem is solved to find an optimal linear combination of estimators that minimizes the variance of the linearly combined estimator. For all classes of estimators, we provide Monte Carlo examples to show that the estimators perform as well in practice as advertised by the theory.

En physique statistique, l’information macroscopique d’intérêt pour les systèmes considérés peut être dé-duite à partir de moyennes sur des configurations microscopiques réparties selon des mesures de probabilitéµ caractérisant l’état thermodynamique du système. En raison de la haute dimensionnalité du système (quiest proportionnelle au nombre de particules), les configurations sont le plus souvent échantillonnées en util-isant des trajectoires d’équations différentielles stochastiques ou des chaînes de Markov ergodiques pourla mesure de Boltzmann-Gibbs µ, qui décrit un système à température constante. Un processus stochas-tique classique permettant d’échantillonner cette mesure est la dynamique de Langevin. En pratique, leséquations de la dynamique de Langevin ne peuvent pas être intégrées analytiquement, la solution est alorsapprochée par un schéma numérique. L’analyse numérique de ces schémas de discrétisation est maintenantbien maîtrisée pour l’énergie cinétique quadratique standard. Une limitation importante des estimateurs desmoyennes sontleurs éventuelles grandes erreurs statistiques.Sous certaines hypothèsessur lesénergies ciné-tique et potentielle, il peut être démontré qu’un théorème de limite central est vrai. La variance asymptotiquepeut être grande en raison de la métastabilité du processus de Langevin, qui se produit dès que la mesure deprobabilité µ est multimodale.Dans cette thèse, nous considérons la discrétisation de la dynamique de Langevin modifiée qui améliorel’échantillonnage de la distribution de Boltzmann-Gibbs en introduisant une fonction cinétique plus généraleà la place de la formulation quadratique standard. Nous avons en fait deux situations en tête : (a) La dy-namique de Langevin Adaptativement Restreinte, où l’énergie cinétique s’annule pour les faibles moments,et correspond à l’énergie cinétique standard pour les forts moments. L’intérêt de cette dynamique est que lesparticules avec une faible énergie sont restreintes. Le gain vient alors du fait que les interactions entre lesparticules restreintes ne doivent pas être mises à jour. En raison de la séparabilité des positions et des mo-ments marginaux de la distribution, les moyennes des observables qui dépendent de la variable de positionsont égales à celles calculées par la dynamique de Langevin standard. L’efficacité de cette méthode résidedans le compromis entre le gain de calcul et la variance asymptotique des moyennes ergodiques qui peutaugmenter par rapport à la dynamique standards car il existe a priori plus des corrélations dans le tempsen raison de particules restreintes. De plus, étant donné que l’énergie cinétique est nulle sur un ouvert, ladynamique de Langevin associé ne parvient pas à être hypoelliptique. La première tâche de cette thèse est deprouver que la dynamique de Langevin avec une telle énergie cinétique est ergodique. L’étape suivante con-siste à présenter une analyse mathématique de la variance asymptotique de la dynamique AR-Langevin. Afinde compléter l’analyse de ce procédé, on estime l’accélération algorithmique du coût d’une seule itération,en fonction des paramètres de la dynamique. (b) Nous considérons aussi la dynamique de Langevin avecdes énergies cinétiques dont la croissance est plus que quadratique à l’infini, dans une tentative de réduire lamétastabilité. La liberté supplémentaire fournie par le choix de l’énergie cinétique doit être utilisée afin deréduire la métastabilité de la dynamique. Dans cette thèse, nous explorons le choix de l’énergie cinétique etnous démontrons une convergence améliorée des moyennes ergodiques sur un exemple de faible dimension.Un des problèmes avec les situations que nous considérons est la stabilité des régimes discrétisés. Afind’obtenir une méthode de discrétisation faiblement cohérente d’ordre 2 (ce qui n’est plus trivial dans le casde l’énergie cinétique générale), nous nous reposons sur les schémas basés sur des méthodes de Metropolis. / In statistical physics, the macroscopic information of interest for the systems under consideration can beinferred from averages over microscopic configurations distributed according to probability measures µcharacterizing the thermodynamic state of the system. Due to the high dimensionality of the system (whichis proportional to the number of particles), these configurations are most often sampled using trajectories ofstochastic differential equations or Markov chains ergodic for the probability measure µ, which describesa system at constant temperature. One popular stochastic process allowing to sample this measure is theLangevin dynamics. In practice, the Langevin dynamics cannot be analytically integrated, its solution istherefore approximated with a numerical scheme. The numerical analysis of such discretization schemes isby now well-understood when the kinetic energy is the standard quadratic kinetic energy.One important limitation of the estimators of the ergodic averages are their possibly large statisticalerrors.Undercertainassumptionsonpotentialandkineticenergy,itcanbeshownthatacentrallimittheoremholds true. The asymptotic variance may be large due to the metastability of the Langevin process, whichoccurs as soon as the probability measure µ is multimodal.In this thesis, we consider the discretization of modified Langevin dynamics which improve the samplingof the Boltzmann–Gibbs distribution by introducing a more general kinetic energy function U instead of thestandard quadratic one. We have in fact two situations in mind:(a) Adaptively Restrained (AR) Langevin dynamics, where the kinetic energy vanishes for small momenta,while it agrees with the standard kinetic energy for large momenta. The interest of this dynamics isthat particles with low energy are restrained. The computational gain follows from the fact that theinteractions between restrained particles need not be updated. Due to the separability of the positionand momenta marginals of the distribution, the averages of observables which depend on the positionvariable are equal to the ones computed with the standard Langevin dynamics. The efficiency of thismethod lies in the trade-off between the computational gain and the asymptotic variance on ergodic av-erages which may increase compared to the standard dynamics since there are a priori more correlationsin time due to restrained particles. Moreover, since the kinetic energy vanishes on some open set, theassociated Langevin dynamics fails to be hypoelliptic. In fact, a first task of this thesis is to prove thatthe Langevin dynamics with such modified kinetic energy is ergodic. The next step is to present a math-ematical analysis of the asymptotic variance for the AR-Langevin dynamics. In order to complementthe analysis of this method, we estimate the algorithmic speed-up of the cost of a single iteration, as afunction of the parameters of the dynamics.(b) We also consider Langevin dynamics with kinetic energies growing more than quadratically at infinity,in an attempt to reduce metastability. The extra freedom provided by the choice of the kinetic energyshould be used in order to reduce the metastability of the dynamics. In this thesis, we explore thechoice of the kinetic energy and we demonstrate on a simple low-dimensional example an improvedconvergence of ergodic averages.An issue with the situations we consider is the stability of discretized schemes. In order to obtain aweakly consistent method of order 2 (which is no longer trivial for a general kinetic energy), we rely on therecently developped Metropolis schemes.

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy pure-jump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using mean-variance hedging and dynamic programming.

Par un développement en série de Taylor, une relation analytique générale est établie pour calculer l’incertitude de la réponse du modèle, en assumant l'indépendance des entrées. En utilisant des relations de puissances et exponentielles, il est démontré que l’approximation souvent utilisée permet d’évaluer de manière satisfaisante l’incertitude sur la réponse du modèle pourvu que l’incertitude d’entrée soit négligeable ou que le modèle soit presque linéaire. La méthode est appliquée à l’étude d’un réseau de distribution électrique et à un modèle d’ordre économique.La méthode est étendue aux cas où les variables d’entrée sont corrélées. Avec la méthode généralisée, on peux déterminer si les corrélations d'entrée doivent ou non être considérées pour des applications pratiques. Des exemples numériques montrent l'efficacité et la validation de notre méthode dans l'analyse des modèles tant généraux que spécifiques tels que le modèle déterministe du VIH. La méthode est ensuite comparée à celle de Sobol. Les résultats montrent que la méthode de Sobol peut surévaluer l’incidence des divers facteurs, mais sous-estimer ceux de leurs interactions dans le cas d’interactions non linéaires entre les paramètres d’entrée. Une modification est alors introduite, aidant à comprendre la différence entre notre méthode et celle de Sobol. Enfin, un modèle numérique est établi dans le cas d’un jeu virtuel prenant en compte la formation de la dynamique de l'opinion publique. L’analyse théorique à l’aide de la méthode de modification d'un paramètre à la fois. La méthode basée sur l'échantillonnage fournit une analyse globale de l'incertitude et de la sensibilité des observations. / By means of taylor series expansion, a general analytic formula is derived to characterise the uncertaintypropagation from input variables to the model response,in assuming input independence. By using power-lawand exponential functions, it is shown that the widelyused approximation considering only the first ordercontribution of input uncertainty is sufficiently good onlywhen the input uncertainty is negligible or the underlyingmodel is almost linear. This method is then applied to apower grid system and the eoq model.The method is also extended to correlated case. Withthe extended method, it is straightforward to identify theimportance of input correlations in the model response.This allows one to determine whether or not the inputcorrelations should be considered in practicalapplications. Numerical examples suggest theeffectiveness and validation of our method for generalmodels, as well as specific ones such as thedeterministic hiv model.The method is then compared to Sobol’s one which isimplemented with sampling based strategy. Resultsshow that, compared to our method, it may overvaluethe roles of individual input factors but underestimatethose of their interaction effects when there arenonlinear coupling terms of input factors. A modificationis then introduced, helping understand the differencebetween our method and Sobol’s one.Finally, a numerical model is designed based on avirtual gambling mechanism, regarding the formation ofopinion dynamics. Theoretical analysis is proposed bythe use of one-at-a-time method. Sampling-basedmethod provides a global analysis of output uncertaintyand sensitivity.

A avicultura é uma das principais atividades agropecuárias do Brasil, em 2011 o país produziu 12.230 toneladas de carne de frango, sendo o 3º maior produtor de frango do mundo, apenas atrás dos EUA e China. Parte deste êxito se deve principalmente ao melhoramento genético animal implantado nas últimas décadas. Os objetivos nesse estudo foram: 1º - Comparar as funções das curvas de crescimento: von Bertalanffy, Gompertz, Logística, Richards e Brody, pelo método dos Mínimos Quadrados Ordinários (QMO) e Quadrados Mínimos Ponderados (QMP) a dados de peso vivo para as linhagens experimentais de frango caipira (7P, Caipirão da ESALQ, Caipirinha da ESALQ e Carijó Barbado) e selecionar uma curva de crescimento que melhor descreva o padrão de crescimento para cada linhagem, e estimar os componentes genéticos (herdabilidades e correlações genéticas) dos parâmetros destas funções sob análise bicaracterística; 2º - Comparar modelos com diferentes ordens de ajuste por meio de funções polinomiais de Legendre, sob modelos de regressão aleatória, com variância residual heterogênea, para a estimação dos componentes de (co) variância e avaliação genética de linhagens experimentais de frango caipira (7P, Caipirão da ESALQ, Caipirinha da ESALQ e Carijó Barbado). O modelo que melhor se adequou a curva de crescimento para as linhagens estudadas foi à função de Gompertz ajustado pelo método dos Quadrados Mínimos Ponderados (QMP). Os parâmetros genéticos estimados para as medidas e dos modelos Gompertz ponderado podem ser utilizados como critérios de seleção, pois parecem ter efeito genético considerável para estas características. No entanto, deve-se haver cautela na utilização do parâmetro como critério de seleção para a linhagem Carijó Barbado devido a baixa herdabilidade. As correlações genéticas e fenotípicas entre as características e foram negativas e altas. Indicando que quanto maior o peso assintótico menor a taxa de crescimento. Dentre os modelos de Regressão Aleatória estudados o polinômio de 3ª ordem foi o que melhor se adequou para descrever as curvas de crescimento das linhagens estudadas. As estimativas de variâncias, herdabilidades foram afetadas pela modelagem da variância residual. Em geral as herdabilidades estimadas para as idades de 1 a 84 dias variaram de moderadas a altas para as linhagens estudadas, indicando que qualquer idade pode ser utilizada como critério de seleção. A seleção aos 42 dias de idade pode ser mantida como critério de seleção. / Aviculture is one of the main agribusiness activities in Brazil, in 2011 the country produced 12,230 tons of broiler meat, was the 3rd largest producer of broiler in the world, only behind the USA and China. Part of this success is mainly due to animal genetic improvement implemented in recent decades. In this study, our objectives were: 1 - to compare the functions of the Von Bertalanffy, Gompertz, Logistic, Richards and Brody growth curves by the Ordinary Least Squares and Weighted Least Squares method, from data for body weight from experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado) and select a growth curve that best describes their growth. From this, estimates of the genetic components (heritability and genetic correlations) of the parameters of these functions under bivariate analysis; 2 - Comparing models with different orders of adjustment by means of Legendre polynomial functions under random regression models with heterogeneous residual variance for the estimation of (co) variance and genetic evaluation of experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado). The model that best adapted the growth curve for all lines studied was the Gompertz function adjusted using weighted least squares. Genetic parameters for measurements and can be used as selection criteria because they seem to have considerable genetic effects for these characteristics. There should be caution in using the parameter as a selection criterion for the Carijó Barbado line due to low heritability. The genetic and phenotypic correlations between traits and were negative and high, indicating that the higher the asymptotic weight, the lower the growth rate. Among the Random Regression models studied the 3rd order polynomial was best adapted to describe the growth curves of the lines studied. Estimates of variances and heritabilities were affected by residual variance modeling. Overall heritability estimates between 1 to 84 days of age ranged from moderate to high for all lines, indicating that any age can be used as a selection criterion, including maintaining the current selection at 42 days of age.

Submitted by (edna.saturno@ufrpe.br) on 2017-05-18T13:59:13Z No. of bitstreams: 1 Tatiana Neres de Oliveira.pdf: 1588049 bytes, checksum: 1bec51e391cc99844e14b24b53268967 (MD5) / Made available in DSpace on 2017-05-18T13:59:13Z (GMT). No. of bitstreams: 1 Tatiana Neres de Oliveira.pdf: 1588049 bytes, checksum: 1bec51e391cc99844e14b24b53268967 (MD5) Previous issue date: 2007-03-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The work was conducted at the Itambé Experimental Station of the Pernambuco State Agricultural Research Enterprise – IPA, to characterize clones and estimate heritability and character correlation, besides estimate repeatability coefficients and evaluate adaptability and stability of eye spot incidence in Pennisetum sp. clones under pasture. Sixteen Pennisetum sp. clones were studied under pasture at 42 days intervals, and after-grazing residual of 40 cm, under the randomized blocks design, with five replicates. Characters evaluated before grazing were forage availability, average plant height, disease incidence, desirability, uncovered soil, above and below 40 cm forage mass. Residual biomass above and below 40 cm, average plant height and losses were evaluated after grazing. Heritability was estimated on the ample sense, and averages were compared by theTukey test at five percent significance. Clones Taiwan A 25 P 18 (3.8), Pusa Napier 1 P 32 (1.8), SEA P 35 (1.8), SEA P 36 (3.4), SEA P 37 (3.2), RENACE CNPGL 93F41.1 (2.0), hybrids HV 241 (1.8) and Pioneiro (2.4) had the highest Helminthosporium susceptibility notes. Except for leaf production, below 40 cm residual biomass, and after grazing losses, all evaluated variables had highheritability value (64.75 to 93.40%). Choosing higher plants leads to simultaneous selection for higher above 40 cm forage mass, desirability, lower disease incidence and higher soil coverage index. Repeatability coefficients were estimated by: analysis of variance, principal components – correlation matrix, principal components – covariance matrix, and structural analysis – correlation matrix. Maximum heritability for leaf spot was 95 %. Repeatability coefficients by the four methods ranged from 0.75 to 0.78. With regards to genotype adaptability, Mineirão (0.31), Taiwan A 25 P 18 (0.50), SEA P 36 (0.28), SEA P 37 (0.38) and Gigante de Pinda P 73 (0.46) had regression coefficients below population average (β1i), indicating unfavorable environment adaptability. Genotypes Pusa Napier 1 P 25 (1.58), Pusa Napier 1 P 27 (1.55), Pusa Napier 1 P 28 (1.47), Pusa Napier 1 P 32(1.28), Pusa Napier 1 P 33 (1.22), SEA P 35 (1.60), HV 241 (1.41) and Pioneiro (1.36) had better response in favorable environments, and Pusa Napier 1 P 31 and Roxo de Botucatu P 80 had ample adaptability. Hybrid HV 241 and Pioneiro had significant deviations from regression by the F test (P<0.05), indicating instability and unpredictability to environmental alterations. / O trabalho foi realizado na Estação Experimental de Itambé da Empresa Pernambucana de Pesquisa Agropecuária – IPA, objetivando caracterizar clones e estimar a herdabilidade e correlações, além de estimar coeficientes de repetibilidade e avaliar a adaptabilidade e estabilidade de clones de Pennisetum sp. sob pastejo a incidência de mancha ocular. Foram estudados 16 clones de Pennisetum sp. sob pastejo a intervalos de 42 dias e resíduo pós pastejo de 40 cm, num delineamento em blocos ao acaso, com cinco repetições. Os caracteres avaliados no pré pastejo foram disponibilidade de forragem, altura média das plantas, incidência de doença, desejabilidade, solo descoberto, massa de forragem acima e abaixo de 40 cm. Biomassa residual acima e abaixo de 40 cm, altura média das plantas e perdas foram avaliadas no pós pastejo. Os coeficientes de repetibilidade foram estimados por:análise de variância, componentes principais – matriz de correlação, componentes principais – matriz de covariância e análise estrutural – matriz de correlação. A herdabilidade foi estimada no sentido amplo e as médias comparadas pelo teste de Tukey a 5% de probabilidade. Os clones Taiwan A 25 P 18 (3,8), Pusa Napier 1 P 32 (1,8), SEA P 35 (1,8), SEA P 36 (3,4), SEA P 37 (3,2), RENACE CNPGL 93F41.1(2,0), o híbrido HV 241 (1,8) e o Pioneiro (2,4) apresentaram maiores notas para susceptibilidade ao Helminthosporium. Com exceção de produção de folhas, biomassa residual abaixo de 40 cm e perdas pós pastejo, todas as variáveis analisadas apresentaram valores altos para herdabilidade (64,75 a 93,4%). A escolha de plantas mais altas leva à seleção simultânea para maior produção de massa de forragem acima de 40 cm e desejabilidade, menor incidência de doenças e maior índice de cobertura do solo. O valor máximo da herdabilidade para mancha ocular foi de 95%. Os coeficientes de repetibilidade estimados pelos quatro métodos variaram de 0,75 a 0,78. Com relação à adaptabilidade dos genótipos, o Mineirão (0,31), Taiwan A 25 P 18 (0,50), SEA P 36 (0,28), SEA P 37 (0,38) e Gigante de Pinda P 73 (0,46) apresentaram coeficientes de regressão abaixo da média populacional (β1i), indicandoadaptabilidade a ambientes desfavoráveis. Os genótipos Pusa Napier 1 P 25 (1,58), Pusa Napier 1 P 27 (1,55), Pusa Napier 1 P 28 (1,47), Pusa Napier 1 P 32 (1,28), Pusa Napier 1 P 33 (1,22), SEA P 35 (1,60), HV 241 (1,41) e Pioneiro (1,36) responderam melhor em ambientes favoráveis, e o Pusa Napier 1 P 31 e Roxo de Botucatu P 80 apresentaram ampla adaptabilidade. O híbrido HV 241 e o Pioneiro apresentaram desvios significativos da regressão pelo teste F (P<0,05), sugerindo instabilidade e imprevisibilidade às alterações ambientais.

Esse trabalho teve como objetivo comparar métodos de estimação de componentes de variância e parâmetros genéticos, considerando tanto o delineamento estatístico fatorial instalado em látice quadrado como o delineamento genético III. Como referência, foram utilizados três conjuntos de dados reais, em melhoramento genético de milho, relativos aos caracteres de produção de grãos (gramas por parcela), altura da folha bandeira ao chão (centímetros) e o número de folhas entre a primeira espiga e o pendão; sendo que a altura da folha bandeira e o número de folhas foram obtidos pela média entre cinco plantas competitivas para cada parcela. O método da Análise da Variância (ANOVA), conforme indicado pelo Delineameno III, foi utilizado na análise dos dados e estimação dos componentes de variância relativos ao modelo matemático, variâncias genéticas, coeficiente de herdabilidade e grau médio de dominância para cada um dos três caracteres estudados. Essas estimativas foram utilizadas na simulação de 1000 conjuntos de dados com características semelhantes a cada um dos conjuntos de dado reais considerados. Os métodos da ANOVA e da máxima verossimilhança restrita (REML) foram utilizados na predição dos parâmetros já mencionados para cada um dos conjuntos de dados simulados dentro de cada caráter. As 1000 estimativas obtidas por cada método, para cada caráter estudado, foram utilizadas no cálculo de estatísticas descritivas (média, desvio-padrão e acurácia relativa) e na montagem de gráficos de Box-plot. Utilizando as informações obtidas a partir das estimativas fornecidas por cada método e em posse dos valores reais que essas estimativas deveriam prever (valor utilizado na simulação dos dados) foi possível comparar ambos os métodos quanto à eficiência das estimativas por eles fornecidas. Ambos os métodos apresentaram características semelhantes na predição da maioria dos componentes de variância relativos ao modelo matemático, sendo que as maiores disparidades se deram para os componentes relativos aos efeitos de progênie (?p2) e as interações entre progênie e linhagem (?pt2) e entre progênie, linhagem e ambiente (?pta2); os quais são os componentes de maior peso no cálculo das variâncias e parâmetros genéticos. O método da ANOVA foi o bastante eficiente na predição de ?p2, sendo que o método da REML se aproxima dos resultados obtidos pelo método da ANOVA conforme diminuem os valores de referência para esse componente; para ?pt2 o método da REML se mostrou mais eficiente conforme maior é o valor de referência, porém, perde eficiência e se aproxima do método da ANOVA conforme o valor de referência do componente diminui. Ambos os métodos se mostraram ineficientes na predição de ?pta2, porém o método da REML foi o menos eficiente. O melhor desempenho do método da ANOVA na predição dos componentes de variância de maior peso no cálculo das variâncias genéticas levou a um melhor desempenho desse método na predição de todos os parâmetros genéticos, com exceção da variância de dominância, a qual depende unicamente de ?pt2. Porém, foi observada uma tendência no método da ANOVA, em média, na superestimação do grau médio de dominância em cerca de 45% do seu valor de referência, independentemente do caráter estudado. / This work aimed to compare estimation methods for variance components and genetic parameters, considering the factorial statistical design set in randomized blocks and the genetic Design III. As reference, three sets of real data were used, on maize genetic improvement, related to the characters: grain yield (grams by plot), plant height, measured from the ground to the °ag leaf in centimeters, and the number of leaves above the uppermost ear. The analysis of variance method (ANOVA), accordingly to the proposed by the Design III, was used on the analysis of the data and estimation of the variance components derived from the mathematical model, genetic variances, heritability and average degree of dominance for each of the studied characters. This estimatives were used on the simulation of 1000 data sets with similar characteristics to the real data analyzed. The ANOVA and restricted maximum likelihood (REML) methods were used on the prediction of the already mentioned parameters for each of the simulated data sets within each character. The 1000 estimatives obtained by each method, for each studied character, were used on the calculation of descriptive statistics (mean, standard deviation and relative accuracy) and for the ¯tting of box-plot graphics. Through the information obtained from the estimatives given by each method and in possession of the actual values that they should predict (values used in the simulation of the data sets) it was possible to compare both methods as to the e±ciency of the estimatives given by them. Both methods presented similar characteristics on the prediction of most of the variance components derived from the mathematical model, being that most di®erences were pertinent to the components related to the e®ects of progeny (¾2 p) and to the interactions between progeny and parental inbred (¾2 pt) and between progeny, parental inbred and environment (¾2 pta); which are the components of greater importance on the calculation of the genetic parameters. The ANOVA method was very e±cient on the prediction of ¾2 p, being that the smaller the reference value for this component, more the REML method approached the results obtained by the ANOVA method; for larger values of ¾2 pt the most e±cient was the REML method, but its e±ciency decayed and approached the ANOVA method for smaller reference values for this component. Both methods were poorly e±cient on the prediction of ¾2 pta, but the REML method was the least e±cient. The better performance of the ANOVA method on the prediction of the variance components of greater importance on the calculation of the genetic variances lead to a better performance of the ANOVA method on the prediction of all genetic parameters, with exception to the dominance variance, which depended solely on ¾2 pt. However, it was observed a tendency on the ANOVA method, in average, on the overestimation of the average degree of dominance of around 45% of the actual reference value, independently of the studied character.

O conhecimento da base genética dos caracteres é muito importante para orientar os melhoristas quanto às estratégias a serem utilizadas visando uma maior eficiência dos programas de seleção. Para os caracteres quantitativos, o estudo da base genética dos mesmos é geralmente feito através de estimativas de componentes de variância. A maioria dos delineamentos genéticos disponíveis permite estimar a variância genética aditiva e a variância genética dominante. Poucos delineamentos permitem detectar a ocorrência de epistasia e, consequentemente o componente epistático da variância genética. O objetivo deste trabalho foi detectar a ocorrência da epistasia em soja utilizando o Delineamento Trialélico Modificado (\"Modified triple test cross). O material genético utilizado compreendeu uma amostra de 30 linhas puras derivadas do cruzamento entre os genitores PI-123439 e PI-239235. As 30 linhas puras foram cruzadas com dois testadores contrastantes para a produção de grãos, denominados L1 e L2, gerando, portanto, 60 cruzamentos. Os cruzamentos foram autofecundados, a fim de multiplicar as sementes para a realização dos experimentos, obtendo-se, portanto, a geração F2 dos 60 cruzamentos. No ano agrícola de 2003/2004 os tratamentos foram avaliados em um experimento em blocos ao acaso com 15 repetições, contendo 90 tratamentos, isto é, os 60 cruzamentos, e as 30 linhagens. No ano agrícola de 2004/2005 foi feita uma nova avaliação experimental, de maneira semelhante ao ano anterior, utilizando como tratamentos os \"bulks\" de cada tratamento da geração anterior (geração F3). Em todos os casos as parcelas experimentais foram constituídas de uma linha de dois metros, com espaçamento entre linhas de 0,50 metros, contendo 35 plantas no estande ideal. Foram avaliados os seguintes caracteres: produção de grãos (PG), altura da planta no florescimento (AF), altura da planta na maturação (AM), dias para o florescimento (DF) e dias para a maturação (DM). Os dados experimentais foram submetidos às análises de variância e em seguida a uma análise genética, segundo o Delineamento Trialélico Modificado, que foi adaptado para as gerações F2 e F3. Os resultados indicaram a ocorrência de epistasia para PG, DF e DM, mas não para AF. Quanto ao caráter AM, não foi possível tirar conclusões, sendo necessário mais estudos. Estes resultados indicam que as estimativas de variâncias genéticas aditivas e dominantes para caracteres como PG, DF e DM em soja podem ser viesadas, quando não se considera a epistasia no modelo. / The understanding of the nature of genetic traits is very important in guiding plant breeders in designing strategies aiming to increase efficiency of selection programmes. The study of the genetic basis of quantitative traits is generally done through estimates of variance. The majority of genetic tests currently available permit the estimate of both additive and dominant genetic variance. Few tests detect the occurrence of epistasis and consequently the epistatic component of genetic variance. The objective of this work was to detect the occurrence of epistatis in soybean by using the \"Modified triple test cross\". The genetic material utilized consisted of a sample of 30 pure lines derived from a cross between the genitors PI-123439 and PI239235. The 30 pure lines were crossed with two contrasting test individuals to produce seed, which was denominated L1 and L2, generated from a total of 60 crosses. The progeny were self-crossed to multiply the seeds in order to carry out the experiments, producing an F2 generation of the 60 crosses. In the agricultural year 2003-2004 the measurements were carried out in an experiment of random plots with 15 repetitions, totalling 90 sets. In the agricultural year 2004-2005 further experiments were carried out, and measurements were taken using plants from the bulked F3 seed. In all cases the experimental plots consisted of a line of two metres, with a space between lines of 0.5 metres, totalling an average of 35 plants. The following traits were evaluated: grain yield, inflorescence height, plant height at maturation, age at flowering and maturation. The experimental data was subjected to analyses of genetic variance, followed by genetic analysis and the \"Modified triple test cross\" that was adapted for the F2 and F3 generations. The results indicate the occurrence of epistasis for grain yield, age at flowering and maturation, but not for plant height at flowering. It was not possible to determine if the trait for plant height at maturation showed epistasis, further experiments need to be carried out. These results suggest that the estimates of genetic additive and dominant variance for the grain yield, age at flowering and maturation traits in soybean may be incorrect when epistasis is not considered in the model.