This dissertation focuses on issues related to fitting an optimal variance-covariance structure in multilevel linear modeling framework with two Monte Carlo simulation studies. In the first study, the author evaluated the performance of common fit statistics such as Likelihood Ratio Test (LRT), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) and a new proposed method, standardized root mean square residual (SRMR), for selecting the correct within-subject covariance structure. Results from the simulated data suggested SRMR had the best performance in selecting the optimal covariance structure. A pharmaceutical example was also used to evaluate the performance of these fit statistics empirically. The LRT failed to decide which is a better model because LRT can only be used for nested models. SRMR, on the other hand, had congruent result as AIC and BIC and chose ARMA(1,1) as the optimal variance-covariance structure. In the second study, the author adopted a first-order autoregressive structure as the true within-subject V-C structure with variability in the intercept and slope (estimating [tau]00 and [tau]11 only) and investigated the consequence of misspecifying different levels/types of the V-C matrices simultaneously on the estimation and test of significance for the growth/fixed-effect and random-effect parameters, considering the size of the autoregressive parameter, magnitude of the fixed effect parameters, number of cases, and number of waves. The result of the simulation study showed that the commonly-used identity within-subject structure with unstructured between-subject matrix performed equally well as the true model in the evaluation of the criterion variables. On the other hand, other misspecified conditions, such as Under G & Over R conditions and Generally misspecified G & R conditions had biased standard error estimates for the fixed effect and lead to inflated Type I error rate or lowered statistical power. The two studies bridged the gap between the theory and practical application in the current literature. More research can be done to test the effectiveness of proposed SRMR in searching for the optimal V-C structure under different conditions and evaluate the impact of different types/levels of misspecification with various specifications of the within- and between- level V-C structures simultaneously.

"Practical usage of optimal portfolio diversification using maximum entropy principle" by Ostap Chopyk Abstract This thesis enhances the investigation of the principle of maximum entropy, implied in the portfolio diversification problem, when portfolio consists of stocks. Entropy, as a measure of diversity, is used as the objective function in the optimization problem with given side constraints. The principle of maximum entropy, by the nature itself, suggests the solution for two problems; it reduces the estimation error of inputs, as it has a shrinkage interpretation and it leads to more diversified portfolio. Furthermore, improvement to the portfolio optimization is made by using design-free estimation of variance-covariance matrices of stock returns. Design-free estimation is proven to provide superior estimate of large variance-covariance matrices and for data with heavy-tailed densities. To asses and compare the performance of the portfolios, their out-of-sample Sharpe ratios are used. In nominal terms, the out-of- sample Sharpe ratios are almost always lower for the portfolios, created using maximum entropy principle, than for 'classical' Markowitz's efficient portfolio. However, this out-of-sample Sharpe ratios are not statistically different, as it was tested by constructing studentized time-series...

Nos programas de melhoramento de cana-de-açúcar todos os anos são instalados experimentos com o objetivo de avaliar genótipos que podem eventualmente ser recomendados para o plantio, ou mesmo como genitores. Este objetivo é atingido com o emprego de experimentos em diferentes locais, durante diferentes colheitas. Além disso, frequentemente há grande desbalanceamento, pois nem todos os genótipos são avaliados em todos os experimentos. O emprego de abordagens tradicionais como análise de variância conjunta (ANAVA) é inviável devido à condição de desbalanceamento e ao fato de as pressuposições não modelarem adequadamente o relacionamento entre as observações. O emprego de modelos misto utilizando a metodologia REML/BLUP é uma alternativa para análise desses experimentos em cana-deaçúcar, permitindo também incorporar a informação de parentesco entre os indivíduos. Nesse contexto, foram analisados 44 experimentos (locais) de cana-de-açúcar do programa de melhoramento da cana-de-açúcar do Instituto Agronômico de Campinas (IAC), com 74 genótipos (clones e variedades) e com até 5 colheitas. O delineamento foi o de blocos ao acaso com 2 a 6 repetições. O caráter analisado foi TPH (Tonelada de pol por hectare). Foram testados 40 modelos, os 20 primeiros foram avaliadas diferentes estrutura de VCOV para locais e colheitas, e os 20 seguintes, além das matrizes de VCOV, foi incorporada a matriz de parentesco genético, A. De acordo com AIC, verificou-se que o Modelo 11, o qual assume as matrizes FA1, AR1 e ID, para locais, colheitas e genótipos, respectivamente, foi o melhor, e portanto, o mais eficiente para seleção de genótipos superiores. Quando comparado ao modelo tradicional (médias dos experimentos), houve mudanças no ranqueamento dos genótipos. Há correlação entre o modelo tradicional e o Modelo 11 (_ = 0, 63, p-valor < 0, 001). A opção de utilizar modelo misto sem ajustar as matrizes de VCOV (Modelo 1) é relativamente melhor do que usar o Modelo Tradicional. Isto foi evidenciado pela correlação mais alta entre os modelos 1 e 11 (_ = 0, 87 com p-valor < 0, 001). Acredita-se que o emprego do Modelo 11 junto com experiência do melhorista poderá aumentar a eficiência de seleção em programas de melhoramento de cana-de-açúcar. / In breeding programs of sugarcane every year experiments are installed to evaluate the performance of genotypes, in order to select superior varieties and genitors. The use of ordinary approaches such as joint analysis of variance (ANOVA) is unfeasible due to unbalancing and assumptions that do not reflect the standard of relationship of the observations. The use of mixed models using the method REML/BLUP is an alternative. It also allows the incorporation of information from kinship between individuals. In this context, we analyzed 44 trials (locations) of sugarcane breeding program of sugarcane (Agronomic Institute Campinas, IAC), with 74 genotypes (varieties and clones), up to 5 harvests. The experimental design was randomized blocks with 2-6 replicates. The character was examined TPH (Tons of pol per hectare). We tested 40 models, the first 20 were evaluated different VCOV structure to locations and harvests, and 20 following addition of matrix VCOV was incorporated genetic relationship matrix, A. Under AIC, it was found that the model 11, which assumes matrices FA1, AR1 and ID for locations, harvests and genotypes, respectively, was the best. There is a moderate correlation between traditional model and model 11 (_ = 0.63, p-value < 0.001), when ranking the genotypes. The option of using mixed model without adjusting matrices VCOV (model 1) is better than using the traditional model. This was suggested by the higher correlation between models 1 and 11 (_ = 0.87 with p-value < 0.001). We believe that the usage of model 11 together with breeders experience can increase the efficiency of selection in sugarcane breeding programs.

<p>Radiation quality is described by the RBE (relative biological effectiveness) that varies with the ionizing ability of the radiation. Microdosimetric quantities describe distributions of energy imparted to small volumes and can be related to RBE. This has made microdosimetry a powerful tool for radiation quality determinations in both radiation protection and radiation therapy. The variance-covariance method determines the dose-average of the distributions and has traditionally been used with two detectors to correct for beam intensity variations. Methods to separate dose components in mixed radiation fields and to correct for beam variations using only one detector have been developed in this thesis. Quality factor relations have been optimized for different neutron energies, and a new algorithm that takes single energy deposition events from densely ionizing radiation into account has been formulated. The variance-covariance technique and the new methodology have been shown to work well in the cosmic radiation field onboard aircraft, in the mixed photon and neutron fields in the nuclear industry and in pulsed fields around accelerators.</p><p>The method has also been used for radiation quality characterization in therapy beams. The biological damage is related to track-structure and ionization clusters and requires descriptions of the energy depositions in nanometre sized volumes. It was shown that both measurements and Monte Carlo simulation (condensed history and track-structure) are needed for a reliable nanodosimetric beam characterization. The combined experimental and simulated results indicate that the dose-mean of the energy imparted to an object in the nanometre region is related to the clinical RBE in neutron, proton and photon beams. The results suggest that the variance-covariance technique and the dose-average of the microdosimetric quantities could be well suited for describing radiation quality also in therapy beams.</p>

Radiation quality is described by the RBE (relative biological effectiveness) that varies with the ionizing ability of the radiation. Microdosimetric quantities describe distributions of energy imparted to small volumes and can be related to RBE. This has made microdosimetry a powerful tool for radiation quality determinations in both radiation protection and radiation therapy. The variance-covariance method determines the dose-average of the distributions and has traditionally been used with two detectors to correct for beam intensity variations. Methods to separate dose components in mixed radiation fields and to correct for beam variations using only one detector have been developed in this thesis. Quality factor relations have been optimized for different neutron energies, and a new algorithm that takes single energy deposition events from densely ionizing radiation into account has been formulated. The variance-covariance technique and the new methodology have been shown to work well in the cosmic radiation field onboard aircraft, in the mixed photon and neutron fields in the nuclear industry and in pulsed fields around accelerators. The method has also been used for radiation quality characterization in therapy beams. The biological damage is related to track-structure and ionization clusters and requires descriptions of the energy depositions in nanometre sized volumes. It was shown that both measurements and Monte Carlo simulation (condensed history and track-structure) are needed for a reliable nanodosimetric beam characterization. The combined experimental and simulated results indicate that the dose-mean of the energy imparted to an object in the nanometre region is related to the clinical RBE in neutron, proton and photon beams. The results suggest that the variance-covariance technique and the dose-average of the microdosimetric quantities could be well suited for describing radiation quality also in therapy beams.

Nos programas de melhoramento de cana-de-açúcar todos os anos são instalados experimentos com o objetivo de avaliar genótipos que podem eventualmente ser recomendados para o plantio, ou mesmo como genitores. Este objetivo é atingido com o emprego de experimentos em diferentes locais, durante diferentes colheitas. Além disso, frequentemente há grande desbalanceamento, pois nem todos os genótipos são avaliados em todos os experimentos. O emprego de abordagens tradicionais como análise de variância conjunta (ANAVA) é inviável devido à condição de desbalanceamento e ao fato de as pressuposições não modelarem adequadamente o relacionamento entre as observações. O emprego de modelos misto utilizando a metodologia REML/BLUP é uma alternativa para análise desses experimentos em cana-deaçúcar, permitindo também incorporar a informação de parentesco entre os indivíduos. Nesse contexto, foram analisados 44 experimentos (locais) de cana-de-açúcar do programa de melhoramento da cana-de-açúcar do Instituto Agronômico de Campinas (IAC), com 74 genótipos (clones e variedades) e com até 5 colheitas. O delineamento foi o de blocos ao acaso com 2 a 6 repetições. O caráter analisado foi TPH (Tonelada de pol por hectare). Foram testados 40 modelos, os 20 primeiros foram avaliadas diferentes estrutura de VCOV para locais e colheitas, e os 20 seguintes, além das matrizes de VCOV, foi incorporada a matriz de parentesco genético, A. De acordo com AIC, verificou-se que o Modelo 11, o qual assume as matrizes FA1, AR1 e ID, para locais, colheitas e genótipos, respectivamente, foi o melhor, e portanto, o mais eficiente para seleção de genótipos superiores. Quando comparado ao modelo tradicional (médias dos experimentos), houve mudanças no ranqueamento dos genótipos. Há correlação entre o modelo tradicional e o Modelo 11 (_ = 0, 63, p-valor < 0, 001). A opção de utilizar modelo misto sem ajustar as matrizes de VCOV (Modelo 1) é relativamente melhor do que usar o Modelo Tradicional. Isto foi evidenciado pela correlação mais alta entre os modelos 1 e 11 (_ = 0, 87 com p-valor < 0, 001). Acredita-se que o emprego do Modelo 11 junto com experiência do melhorista poderá aumentar a eficiência de seleção em programas de melhoramento de cana-de-açúcar. / In breeding programs of sugarcane every year experiments are installed to evaluate the performance of genotypes, in order to select superior varieties and genitors. The use of ordinary approaches such as joint analysis of variance (ANOVA) is unfeasible due to unbalancing and assumptions that do not reflect the standard of relationship of the observations. The use of mixed models using the method REML/BLUP is an alternative. It also allows the incorporation of information from kinship between individuals. In this context, we analyzed 44 trials (locations) of sugarcane breeding program of sugarcane (Agronomic Institute Campinas, IAC), with 74 genotypes (varieties and clones), up to 5 harvests. The experimental design was randomized blocks with 2-6 replicates. The character was examined TPH (Tons of pol per hectare). We tested 40 models, the first 20 were evaluated different VCOV structure to locations and harvests, and 20 following addition of matrix VCOV was incorporated genetic relationship matrix, A. Under AIC, it was found that the model 11, which assumes matrices FA1, AR1 and ID for locations, harvests and genotypes, respectively, was the best. There is a moderate correlation between traditional model and model 11 (_ = 0.63, p-value < 0.001), when ranking the genotypes. The option of using mixed model without adjusting matrices VCOV (model 1) is better than using the traditional model. This was suggested by the higher correlation between models 1 and 11 (_ = 0.87 with p-value < 0.001). We believe that the usage of model 11 together with breeders experience can increase the efficiency of selection in sugarcane breeding programs.

This thesis is focused on a theoretical explication of the basic methods of the calculation Value at Risk for the market and credit risk. For the market risk there is in detail developed the variance -- covariance method, historical simulation and Monte Carlo simulation, above all for the nonlinear portfolio. For all methods the assumptions of their applications are highlighted and the comparation of these methods is made too. For the credit risk there is made a theoretical description of CreditMetrics, CreditRisk+ and KMV models. Analytical part is concerned in the quantification of Value at Risk on two portfolios, namely nonlinear currency portfolio, which particular assumptions of the variance -- covariance method a Monte Carlo simulation are tested on. Then by these methods the calculation of Value at Risk is realized. The calculation of Credit Value at Risk is made on the portfolio of the US corporate bonds by the help of CreditMetrics model.

The diploma thesis "Value at Risk: Historical simulation, variance covariance method and Monte Carlo" aims to value the risk which real bond portfolio bears. The thesis is decomposed into two major chapters: Theoretical and Practical chapters. The first one speaks about VaR and conditional VaR theory including their advantages and disadvantages. Moreover, there are described three basic methods to calculate VaR and CVaR with adjustments to each method in order to increase the reliability of results. The last chapter brings results of VaR and CVaR computation. Many graphs, tables and images are added to the result section in order to make the outputs more visible and well-arranged.

>Magister Scientiae - MSc / Financial companies such as investment and commercial banks as well as insurance companies, mutual and pension funds hold assets in the form of financial instruments in portfolios. Nowadays, financial instruments have proliferated so much that there are so many forms of them namely: derivatives, common stock, corporate and government bonds, foreign exchange and contracts. With so many financial instruments, companies can have very large and diversified portfolios for which they must quantify the risk. With high profile calamities that have rocked the financial world lately, the need for better risk management has never been so in demand as before. Value-at-Risk (VaR) is the latest addition in the investor's toolkit as far as measurements of risk is concerned. This new measure of risk complements well the existing risk measures that exist.Unfortunately, VaR is not unanimous and it has attracted a lot of critics over the years. This research thesis is threefold: to introduce the reader to the VaR concept; to discuss the different methods that exist to calculate VaR; and, finally, to simulate the VaR of a portfolio of government bonds. The first part of this research is to introduce the reader to the general idea of risk forms and its management, the role that the existing risk measures have played so far and the coming up of the new technique, which is VaR. The pros and cons that accompany a new technique are discussed as well as the history of VaR. The second part is about the different methods that exist to compute the VaR of a portfolio. Usually, VaR methodologies fall into three categories namely: Parametric; Historical; and Monte Carlo. In this research, the advantages and disadvantages of these three methods are discussed together with a step-wise method on how to proceed to calculate the VaR of a portfolio using any of the three methods. The practical side of this thesis deals about the VaR simulation of a portfolio of financial instruments. The chosen financial instruments are four South African government bonds with different characteristics. VaR for this particular portfolio will then be simulated by the three main methods. Eleven different simulations are run and they are compared against a Control Simulation (Benchmark Portfolio) to see how factors influencing VaR measure cope under different conditions. The main idea here was to check how VaR measures can change under different portfolio characteristics and to interpret these changes. Moreover, the VaR estimates under the three different methods will be compared

Phenotyping in multi-environment trials (MET) plays an important role to access the differential response of maize hybrids across target breeding regions due to genotype by environment (GxE) interaction. In this context, an effective model of genomic selection (GS) to predict the performance of untested hybrids in MET is essential to maximize genetic gains and to efficiently allocated the breeding programs\' budget. Therefore, the goals of this study were (i) to evaluate the predictive accuracies of GBLUP (Genomic Best Linear Unbiased Prediction) models to predict grain yield performance of unobserved tropical maize single-cross hybrids, using models that consider GxE interaction by fitting a factor analytic (FA) variance-covariance (VCOV) structure, and (ii) to investigate the usefulness of genomic relationship information in combination with different VCOV for genetics and residuals effects, under different levels of unbalanced environments. Predictions were performed for two situations: (CV1) untested hybrids, and (CV2) hybrids evaluated in some environments but missing in others. Phenotypic data of grain yield was measured in 156 maize single-cross hybrids at 12 environments. Hybrids genotypes were inferred based on their parents (inbred lines) via SNP (single nucleotide polymorphism) markers obtained from GBS (genotypingby- sequencing). The procedures and models applied in this study can be easily extended to other crops in which MET plays an important role in the breeding process. / A fenotipagem em ensaios de múltiplos ambientes (MET) tem papel importante para acessar a resposta diferencial de híbridos de milho em diferentes regiões alvo de melhoramento, o que se deve a interação genótipos por ambientes (GxE). Neste contexto, um modelo efetivo de seleção genômica (GS) para predição do desempenho de híbridos não avaliados em MET é essencial para maximizar os ganhos genéticos e alocar eficientemente o orçamento dos programas de melhoramento. Desta forma, os objetivos deste estudo foram (i) avaliar as acurácias preditivas de modelos GBLUP (do inglês, Genomic Best Linear Unbiased Prediction) na predição da produtividade de grãos de híbridos simples de milho tropical não avaliados, usando modelos genético-estatísticos que levam em consideração a interação GxE através de uma estrutura de variância-covariância (VCOV) do tipo fator analítico (FA) e (ii) investigar a utilidade da matriz de parentesco realizada em combinação com diferentes estruturas de VCOV para efeitos genéticos e de resíduos em diferentes níveis de ambientes em desbalanceamento. As predições foram realizadas em duas situações: (CV1) híbridos não avaliados em nenhum ambiente e (CV2) híbridos avaliados em alguns ambientes e em outros não. Foram fenotipados 156 híbridos simples de milho em 12 ambientes para a característica produtividade de grãos. O genótipo dos híbridos foi inferido com base nas informações de marcadores SNP (do inglês, single nucleotide polymorphism) das linhagens parentais, obtidos via GBS (do inglês, genotyping-by-sequencing). Os procedimentos e modelos utilizados neste estudo podem ser facilmente estendidos a outras culturas em que MET desempenha um papel importante no processo de melhoramento.