The rapid growth in demand for cellular mobile communications and emerging fixed wireless access has created the need to increase system capacity through more efficient utilization of the frequency spectrum, and the need for better grade of service. In cellular systems, capacity improvement can be achieved by reducing co-channel interference. Several techniques have been proposed in literature for mitigating co-channel interference, such as adaptive antennas and power control. Also, by allocating transmitter power and communication channels efficiently (resource allocation), overall co-channel interference can be maintained below a desired maximum tolerable level, while maximizing the carried traffic of the system. This dissertation presents investigation results on the performance of base station adaptive antennas, power control and channel allocation, as techniques for capacity improvement. Several approaches are analyzed. Firstly, we study the combined use of adaptive antennas and fractional loading factor, in order to estimate the potential capacity improvement achieved by adaptive antennas. Next, an extensive simulation analysis of a cellular network is carried out aiming to investigate the complex interrelationship between power control, channel allocation and adaptive antennas. In the first part of this simulation analysis, the combined use of adaptive antennas, power control and reduced cluster size is analyzed in a cellular system using fixed channel allocation. In the second part, we analyze the benefits of combining adaptive antennas, dynamic channel allocation and power control. Two representative channel allocation algorithms are considered and analyzed regarding how efficiently they transform reduced co-channel interference into higher carried traffic. Finally, the spatial filtering capability of adaptive antennas is used to allow several users to share the same channel within the same cell. Several allocation algorithms combined with power control are analyzed. / Ph. D.

Neste trabalho são apresentadas algumas extensões dos modelos potência-alfa assumindo o contexto em que as observações estão censuradas ou limitadas. Inicialmente propomos um novo modelo assimétrico que estende os modelos t-assimétrico (Azzalini e Capitanio, 2003) e t-potência (Zhao e Kim, 2016) e inclui a distribuição t de Student como caso particular. Este novo modelo é capaz de ajustar dados com alto grau de assimetria e curtose, ainda maior do que os modelos t-assimétrico e t-potência. Em seguida estendemos o modelo t-potência às situações em que os dados apresentam censura, com alto grau de assimetria e caudas pesadas. Este modelo generaliza o modelo de regressão linear t de Student para dados censurados por Arellano-Valle et al. (2012). O trabalho também introduz o modelo linear misto normal-potência para dados assimétricos. Aqui a inferência estatística é realizada desde uma perspectiva clássica usando o método de máxima verossimilhança junto com o método de integração numérica de Gauss-Hermite para aproximar as integrais envolvidas na função de verossimilhança. Mais tarde, o modelo linear com interceptos aleatórios para dados duplamente censurados é estudado. Este modelo é desenvolvido sob a suposição de que os erros e os efeitos aleatórios seguem distribuições normal-potência e normal- assimétrica. Para todos os modelos estudados foram realizados estudos de simulação a fim de estudar as suas bondades de ajuste e limitações. Finalmente, ilustram-se todos os métodos propostos com dados reais. / In this work some extensions of the alpha-power models are presented, assuming the context in which the observations are censored or limited. Initially we propose a new asymmetric model that extends the skew-t (Azzalini e Capitanio, 2003) and power-t (Zhao e Kim, 2016) models and includes the Students t-distribution as a particular case. This new model is able to adjust data with a high degree of asymmetry and cursose, even higher than the skew-t and power-t models. Then we extend the power-t model to situations in which the data present censorship, with a high degree of asymmetry and heavy tails. This model generalizes the Students t linear censored regression model t by Arellano-Valle et al. (2012) The work also introduces the power-normal linear mixed model for asymmetric data. Here statistical inference is performed from a classical perspective using the maximum likelihood method together with the Gauss-Hermite numerical integration method to approximate the integrals involved in the likelihood function. Later, the linear model with random intercepts for doubly censored data is studied. This model is developed under the assumption that errors and random effects follow power-normal and skew-normal distributions. For all the models studied, simulation studies were carried out to study their benefits and limitations. Finally, all proposed methods with real data are illustrated.

Neste trabalho são apresentadas algumas extensões dos modelos potência-alfa assumindo o contexto em que as observações estão censuradas ou limitadas. Inicialmente propomos um novo modelo assimétrico que estende os modelos t-assimétrico (Azzalini e Capitanio, 2003) e t-potência (Zhao e Kim, 2016) e inclui a distribuição t de Student como caso particular. Este novo modelo é capaz de ajustar dados com alto grau de assimetria e curtose, ainda maior do que os modelos t-assimétrico e t-potência. Em seguida estendemos o modelo t-potência às situações em que os dados apresentam censura, com alto grau de assimetria e caudas pesadas. Este modelo generaliza o modelo de regressão linear t de Student para dados censurados por Arellano-Valle et al. (2012). O trabalho também introduz o modelo linear misto normal-potência para dados assimétricos. Aqui a inferência estatística é realizada desde uma perspectiva clássica usando o método de máxima verossimilhança junto com o método de integração numérica de Gauss-Hermite para aproximar as integrais envolvidas na função de verossimilhança. Mais tarde, o modelo linear com interceptos aleatórios para dados duplamente censurados é estudado. Este modelo é desenvolvido sob a suposição de que os erros e os efeitos aleatórios seguem distribuições normal-potência e normal- assimétrica. Para todos os modelos estudados foram realizados estudos de simulação a fim de estudar as suas bondades de ajuste e limitações. Finalmente, ilustram-se todos os métodos propostos com dados reais. / In this work some extensions of the alpha-power models are presented, assuming the context in which the observations are censored or limited. Initially we propose a new asymmetric model that extends the skew-t (Azzalini e Capitanio, 2003) and power-t (Zhao e Kim, 2016) models and includes the Students t-distribution as a particular case. This new model is able to adjust data with a high degree of asymmetry and cursose, even higher than the skew-t and power-t models. Then we extend the power-t model to situations in which the data present censorship, with a high degree of asymmetry and heavy tails. This model generalizes the Students t linear censored regression model t by Arellano-Valle et al. (2012) The work also introduces the power-normal linear mixed model for asymmetric data. Here statistical inference is performed from a classical perspective using the maximum likelihood method together with the Gauss-Hermite numerical integration method to approximate the integrals involved in the likelihood function. Later, the linear model with random intercepts for doubly censored data is studied. This model is developed under the assumption that errors and random effects follow power-normal and skew-normal distributions. For all the models studied, simulation studies were carried out to study their benefits and limitations. Finally, all proposed methods with real data are illustrated.

Doctor of Philosophy / Department of Statistics / Paul I. Nelson / The null hypothesis of equal distributions, H0 : F1[equals]F2[equals]...[equals]FK , is commonly used to compare two or more treatments based on data consisting of independent random samples. Using this approach, evidence of a difference among the treatments may be reported even though from a practical standpoint their effects are indistinguishable, a longstanding problem in hypothesis testing. The concept of effect size is widely used in the social sciences to deal with this issue by computing a unit-free estimate of the magnitude of the departure from H0 in terms of a change in location. I extend this approach by replacing H0 with hypotheses H0* that state that the distributions {Fi} are possibly different in location and or scale, but close, so that rejection provides evidence that at least one treatment has an important practical effect. Assessing statistical significance under H0* is difficult and typically requires inference in the presence of nuisance parameters. I will use frequentist, Bayesian and Fiducial modes of inference to obtain approximate tests and carry out simulation studies of their behavior in terms of size and power. In some cases a bootstrap will be employed. I will focus on tests based on independent random samples arising from K[greater than and equals]3 normal distributions not required to have the same variances to generalize the K[equals]2 sample parameter P(X1>X2) and non-centrality type parameters that arise in testing for the equality of means.

The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated.

<div>Prediction of player performance is a key component in the construction of baseball team rosters. Traditionally, the problem of predicting seasonal plate appearance outcomes has been approached univariately. That is, focusing on each outcome separately rather than jointly modeling the collection of outcomes. More recently, there has been a greater emphasis on joint modeling, thereby accounting for the correlations between outcomes. However, most of these state of the art prediction models are the proprietary property of teams or industrial sports entities and so little is available in open publications.</div><div><br></div><div>This dissertation introduces a joint modeling approach to predict seasonal plate appearance outcome vectors using a mixed-effects multinomial logistic-normal model. This model accounts for positive and negative correlations between outcomes both across and within player seasons. It is also applied to the important, yet unaddressed, problem of predicting performance for players moving between the Japanese and American major leagues.</div><div><br></div>This work begins by motivating the methodological choices through a comparison of state of the art procedures followed by a detailed description of the modeling and estimation approach that includes model t assessments. We then apply the method to longitudinal multinomial count data of baseball player-seasons for players moving between the Japanese and American major leagues and discuss the results. Extensions of this modeling framework to other similar data structures are also discussed.<br>

By means of a Monte Carlo study, this paper investigates the relative performance of Listwise Deletion, the EM-algorithm and the default algorithm in the MICE-package for R (PMM) in estimating regression coefficients under a left truncated covariate with missing values. The intention is to investigate whether the three frequently used missing data techniques are robust against left truncation when missing values are MCAR or MAR. The results suggest that no technique is superior overall in all combinations of factors studied. The EM-algorithm is unaffected by left truncation under MCAR but negatively affected by strong left truncation under MAR. Compared to the default MICE-algorithm, the performance of EM is more stable across distributions and combinations of sample size and missing rate. The default MICE-algorithm is improved by left truncation but is sensitive to missingness pattern and missing rate. Compared to Listwise Deletion, the EM-algorithm is less robust against left truncation when missing values are MAR. However, the decline in performance of the EM-algorithm is not large enough for the algorithm to be completely outperformed by Listwise Deletion, especially not when the missing rate is moderate. Listwise Deletion might be robust against left truncation but is inefficient.

Os métodos geralmente empregados no mercado para o cálculo de medidas de risco baseiam-se na distribuição adotada para os retornos financeiros. Quando a distribuição Normal é adotada, estas avaliações tendem a subestimar o Value at Risk (valor em risco - VaR), pois a distribuição Normal tem caudas mais leves que as observadas nas séries financeiras. Muitas distribuições alternativas vêm sendo propostas na literatura, contudo qualquer modelo alternativo proposto deve ser avaliado com relação ao esforço computacional gasto para cálculo do valor em risco e comparado à simplicidade proporcionada pelo uso da distribuição Normal. Dessa forma, esta dissertação visa avaliar alguns modelos para cálculo do valor em risco, como a modelagem por quantis empíricos, a distribuição Normal e o modelo autorregressivo (AR), para verificação do melhor ajuste à cauda das distribuições das séries de retornos financeiros, além de avaliar o impacto do VaR para o ano seguinte. Nesse contexto, destaca-se o modelo autorregressivo com heterocedasticidade condicional (ARCH) capaz de detectar a volatilidade envolvida nas séries financeiras de retorno. Esse modelo tem-se mostrado mais eficiente, capaz de gerar informações relevantes aos investidores e ao mercado financeiro, com um esforço computacional moderado. / The most used methods for risk evaluation in the financial market usually depend strongly on the distribution assigned to the financial returns. When we assign a normal distribution, results tend to underestimate the Value at Risk (VaR), since the normal distribution usually has a lighter tail than those from the empirical distribution of financial time series. Many other distributions have been proposed in the literature, but we need to evaluate their computational effort for obtaining the value at risk when compared to the easiness of calculation of the normal distribution. In this work, we compare several models for calculating the value at risk, such as the normal, the empirical-quantile and the autoregressive (AR) models, evaluating their goodness-of-fit to the tail of the distribution of financial return time series and the impact of applying the calculated VaR to the following year. We also highlight the autoregressive conditional heteroskedasticity (ARCH) model due to its performance in detecting the volatility in the series. The ARCH model has proved to be efficient and able to generate relevant information to the investors and to the financial market with a moderate computational cost.

Matrix variate skew elliptically contoured distributions generalize several classes of important distributions. This paper defines and explores matrix variate skew elliptically contoured distributions. In particular, we discuss two stochastic representations of the matrix variate skew elliptically contoured distributions.

This thesis explores the problems of fitting antedependence (AD) models and partial antecorrelation (PAC) models to continuous non-Gaussian longitudinal data. AD models impose certain conditional independence relations among the measurements within each subject, while PAC models characterize the partial correlation relations. The models are parsimonious and useful for data exhibiting time-dependent correlations. Since the relation of conditional independence among variables is rather restrictive, we first consider an autoregressively characterized PAC model with independent asymmetric Laplace (ALD) innovations and prove that this model is an AD model. The ALD distribution previously has been applied to quantile regression and has shown promise for modeling asymmetrically distributed ecological data. In addition, the double exponential distribution, a special case of the ALD, has played an important role in fitting symmetric finance and hydrology data. We give the distribution of a linear combination of independent standard ALD variables in order to derive marginal distributions for the model. For the model estimation problem, we propose an iterative algorithm for the maximum likelihood estimation. The estimation accuracy is illustrated by some numerical examples as well as some longitudinal data sets. The second component of this dissertation focuses on AD multivariate skew normal models. The multivariate skew normal distribution not only shares some nice properties with multivariate normal distributions but also allows for any value of skewness. We derive necessary and sufficient conditions on the shape and covariance parameters for multivariate skew normal variables to be AD(p) for some p. Likelihood-based estimation for balanced and monotone missing data as well as likelihood ratio hypothesis tests for the order of antedependence and for zero skewness under the models are presented. Since the class of skew normal random variables is closed under the addition of independent standard normal random variables, we then consider an autoregressively characterized PAC model with a combination of independent skew normal and normal innovations. Explicit expressions for the marginals, which all have skew normal distributions, and maximum likelihood estimates of model parameters, are given. Numerical results show that these three proposed models may provide reasonable fits to some continuous non-Gaussian longitudinal data sets. Furthermore, we compare the fits of these models to the Treatment A cattle growth data using penalized likelihood criteria, and demonstrate that the AD(2) multivariate skew normal model fits the data best among those proposed models.