We discuss the problem of optimal allocation of the design points of an experiment for the case where the trials may fail with non-zero probability. Numerical results for D-optimal designs are given for estimating the coefficients of a polynomial regression. For small sample sizes these designs may deviate substantially from the corresponding designs in the case of certain response. They can be less efficient, but are less affected by failing trials. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

I examine the market reaction to the announcement of FFO by REITs using abnormal trading volume as a gauge of investors’ reaction. I also address the question of whether FFO provides more useful information to investors than net income. Lastly, I examine whether the quality of private information among traders prior to the announcement of FFO affects the level of abnormal trading volume. Using three different specifications, I find that even though the announcement of FFO leads to abnormal trading, there is no association between the level of abnormal trading volume and the size of the surprise contained in the FFO announcement. I also find, using abnormal returns as a measure of investor response, that FFO explains significantly more variance in abnormal returns than net income suggesting that FFO provides more useful information than net income. Lastly, I use the proportion of institutional holdings as a proxy for the number of informed traders to predict the amount of abnormal trading volume. I find no significant relation between abnormal trading volume and the proportion of institutional holdings. However, when I break down institutional ownership into two broad classifications, I find that the level of abnormal trading volume is significantly positively related to the holdings by mutual funds and investment advisors but negatively related to the holdings of other institutions (pension funds &.endowments, banks and insurance companies). This raises questions of whether the use of an aggregate measure of institutional ownership is appropriate in studies that examine the effect of institutional holdings.

Consider the multiresponse polynomial regression model with one control variable and arbitrary covariance matrix among responses. The present results complement solutions by Krafft and Schaefer (1992) and Imhof (2000), who obtained the n-point D-optimal designs for the multiresponse regression model with one linear and one quadratic. We will show that the D-optimal design is invariant under linear transformation of the control variable. Moreover, the most cases of the exact D-optimal designs on [-1,1] for responses consisting of linear and quadratic polynomials only are derived. The efficiency of the exact D-optimal designs for the univariate quadratic model to that for the above model are also discussed. Some conjectures based on intensively numerical results are also included.

Over the past decades simulation techniques, and in particular finite element method, have been used successfully to predict the response of systems across a whole range of industries including aerospace, automotive, chemical processes, geotechnical engineering and many others. In these numerical analyses, the behaviour of the actual material is approximated with that of an idealised material that deforms in accordance with some constitutive relationships. Therefore, the choice of an appropriate constitutive model that adequately describes the behaviour of the material plays an important role in the accuracy and reliability of the numerical predictions. During the past decades several constitutive models have been developed for various materials. In recent years, by rapid and effective developments in computational software and hardware, alternative computer aided pattern recognition techniques have been introduced to constitutive modelling of materials. The main idea behind pattern recognition systems such as neural network, fuzzy logic or genetic programming is that they learn adaptively from experience and extract various discriminants, each appropriate for its purpose. In this thesis a novel approach is presented and employed to develop constitutive models for materials in general and soils in particular based on evolutionary polynomial regression (EPR). EPR is a hybrid data mining technique that searches for symbolic structures (representing the behaviour of a system) using genetic algorithm and estimates the constant values by the least squares method. Stress-strain data from experiments are employed to train and develop EPR-based material models. The developed models are compared with some of the existing conventional constitutive material models and its advantages are highlighted. It is also shown that the developed EPR-based material models can be incorporated in finite element (FE) analysis. Different examples are used to verify the developed EPR-based FE model. The results of the EPR-FEM are compared with those of a standard FEM where conventional constitutive models are used to model the material behaviour. These results show that EPR-FEM can be successfully employed to analyse different structural and geotechnical engineering problems.

Made available in DSpace on 2017-07-10T17:37:30Z (GMT). No. of bitstreams: 1 Vanessa Decker.pdf: 973220 bytes, checksum: 860f5c5a689313e236f31c29b7b9fbfc (MD5) Previous issue date: 2008-07-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The study objective was to evaluate the effects of light intensities upon the initial development of Leucaena leucocephala seedlings. The study was conducted inside a preservation area around a drinking water well used to supply Marechal Cândido Rondon residents from September, 11st to November, 20st . Seeds collected from mature leucaena trees located on adjacent county (Toledo) were scarifyed and sown in vases. The vases were distributed in the area obeying a entirely randomized design with 13 light intensities (treatments) and 10 replications (vases) totalizing 130 vases. Five and two seedlings per vase were left after thinning executed 10 and 20 daysafter sowing, respectively. Sixty days after the sowing, seedlings were collected for measurements of stem diameter, plant height, number and area of leaves, as well as root, stem and leaves biomasses. Results indicated to exist a polynomial relationship of fourth order between biometric parametersand light intensity; highest significances were calculated for intensities of 643 and 2273 Lux indicating that leucaena can be considered pioneering and tolerant to direct sunlight / O presente trabalho teve por objetivo avaliar o efeito de diferentes intensidades luminosas, proporcionadas por sombreamento natural em área de preservação permanente, no desenvolvimento inicial de mudas de leucena. O experimento foi conduzido na área de Captação 1 do Serviço Autônomo de Água e Esgoto de Marechal Candido Rondon PR, no período de 11 de setembro a 20 de novembro de 2007. As sementes, coletadas de árvores matrizes provenientes de um distrito de Toledo de Toledo PR foram submetidas a quebra de dormência com água a 80°C e semeadas em número de dez por vaso. Os vasos foram distribuídos na área obedecendo a um delineamento inteiramente ao acaso com 13 tratamentos correspondentes às intensidades luminosas e 10 repetições (vasos), totalizando 130 vasos. Após 10 e 20 dias da semeadura foram realizados desbastes, deixando-se 5 e 2 plântulas por vaso, respectivamente. Sessenta dias após a semeadura, as mudas foram coletadas para avaliações biométricas como: diâmetro do caule, altura da planta, número de folhas, área foliar, Massa seca da raiz, caule e folha, além do Índice de Velocidade de Emergência. Os dados foram analisados por meio de análise de variância seguida de teste F e análise de regressão. Os resultados da análise demonstraram existir uma relação polinomial de quarta ordem dos parâmetros biométricos com a intensidade luminosa, em que a resposta da leucena foi mais significativa para intensidades iguais a 643 e 2273Lux. A resposta para menor intensidade luminosa parece demonstrar ser a espécie, secundária e invasora. A resposta para 2273Lux reforça a informação de que é uma espécie que também pode ser considerada pioneira e tolerante ao sol

This research is in three parts with different although related objectives. The first part developed an efficient, modified simulated annealing algorithm to solve the D-optimal (determinant maximization) design problem for 2-way polynomial regression with correlated observations. Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this research, we present an improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with the best design selected from the class of designs that are known to be D-optimal in the uncorrelated case: annealing results had generally higher D-efficiency than the best comparison design, especially when the correlation parameter was well away from 0. The second research objective, using Balanced Incomplete Block Designs (BIBDs), wasto construct weakly universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also constructed approximately weakly universal optimal block designs for the block-structured correlation. Lastly, we developed an improved Particle Swarm Optimization(PSO) algorithm with time varying parameters, and solved D-optimal design for linear regression with it. Then based on that improved algorithm, we combined the non-linear regression problem and decision making, and developed a nested PSO algorithm that finds (nearly) optimal experimental designs with each of the pessimistic criterion, index of optimism criterion, and regret criterion for the Michaelis-Menten model and logistic regression model.

This research is in three parts with different although related objectives. The first part developed an efficient, modified simulated annealing algorithm to solve the D-optimal (determinant maximization) design problem for 2-way polynomial regression with correlated observations. Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this research, we present an improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with the best design selected from the class of designs that are known to be D-optimal in the uncorrelated case: annealing results had generally higher D-efficiency than the best comparison design, especially when the correlation parameter was well away from 0. The second research objective, using Balanced Incomplete Block Designs (BIBDs), wasto construct weakly universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also constructed approximately weakly universal optimal block designs for the block-structured correlation. Lastly, we developed an improved Particle Swarm Optimization(PSO) algorithm with time varying parameters, and solved D-optimal design for linear regression with it. Then based on that improved algorithm, we combined the non-linear regression problem and decision making, and developed a nested PSO algorithm that finds (nearly) optimal experimental designs with each of the pessimistic criterion, index of optimism criterion, and regret criterion for the Michaelis-Menten model and logistic regression model.

We propose an algebraic construction of $(d+1)$-point $D$-optimal designs for $d$th degree polynomial regression with weight function $omega(x)ge 0$ on the interval $[a,b]$. Suppose that $omega'(x)/omega(x)$ is a rational function and the information of whether the optimal support contains the boundary points $a$ and $b$ is available. Then the problem of constructing $(d+1)$-point $D$-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be solved from a system of polynomial equations in those constants. Moreover, the $(d+1)$-point $D$-optimal interior support points are the zeros of a certain polynomial which the coefficients can be computed from a linear system. In most cases the $(d+1)$-point $D$-optimal designs are also the approximate $D$-optimal designs.

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be determined e¡Óciently by standard constrained concave programming algorithms.

Consider the D-optimal designs for a combined polynomial of degree d and trigonometric of order m regression on a partial circle [see Graybill (1976), p. 324]. It is shown that the structure of the optimal design depends only on the length of the design interval and that the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure.