Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 290-293).

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This dissertation considers two approaches for testing hypotheses in unbalanced mixed linear models. The first approach is to construct a design with some type of structure or "partial" balance, so that some of the optimal properties of a completely balanced design hold. It is shown that for a particular type of partially balanced design certain hypothesis tests are optimal. The second approach is to study how the unbalancedness of a design affects a hypothesis test in terms of level and power. Measures of imbalance are introduced and simulation results are presented that demonstrate the relationship of the level and power of a test and the measures. The first part of this thesis focuses on error orthogonal designs which are a type of partially balanced design. It is shown that with an error orthogonal design and under certain additional conditions, ANOVA F-tests about certain linear combinations of the variance components and certain linear combinations of the fixed effects are uniformly most powerful (UMP) similar and UMP unbiased. The ANOVA F-tests for the variance components are also invariant, so that the tests are also UMP invariant similar and UMP invariant unbiased. For certain simultaneous hypotheses about linear combinations of the fixed effects, the ANOVA F-tests are UMP invariant unbiased. The second part of this thesis considers a mixed model with a random nested effect, and studies the effects of an unbalanced design on the level and power of a hypothesis test of the nested variance component being equal to zero. Measures of imbalance are introduced for each of the four conditions necessary to obtain an exact test. Simulations are done for two different models to determine if there is a relationship between any of the measures and the level and power for both a naive test and a test using Satterthwaite's approximation. It is found that a measure based on the coefficients of the expected mean squares is indicative of how a test is performing. This measure is also simple to compute, so that it can easily be employed to determine the validity of the expected level and power. / Graduation date: 1999

The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Statistics and Biostatistics." Includes bibliographical references (p. 59-61).

Diss.--Univ. zu Köln, 2009. / Includes bibliographical references.

Adaptive filters are frequently employed in many applications, such as, system identification, adaptive echo cancellation (AEC), active noise control (ANC), adaptive beamforming, speech signal processing and other related problems, in which the statistic of the underlying signals is either unknown a priori, or slowly-varying. Given the observed signals under study, we shall consider, in this dissertation, the time-varying linear model with Gaussian or contaminated Gaussian (CG) noises. In particular, we focus on recursive local estimation and its applications in linear systems. We base our development on the concept of local likelihood function (LLF) and local posterior probability for parameter estimation, which lead to efficient adaptive filtering algorithms. We also study the convergence performance of these algorithms and their applications by theoretical analyses. As for applications, another important one is to utilize adaptive filters to obtain recursive hypothesis testing and model order selection methods. It is known that the maximum likelihood estimate (MLE) may lead to large variance or ill-conditioning problems when the number of observations is limited. An effective approach to address these problems is to employ various form of regularization in order to reduce the variance at the expense of slightly increased bias. In general, this can be viewed as adopting the Bayesian estimation, where the regularization can be viewed as providing a certain prior density of the parameters to be estimated. By adopting different prior densities in the LLF, we derive the variable regularized QR decomposition-based recursive least squares (VR-QRRLS) and recursive least M-estimate (VR-QRRLM) algorithms. An improved state-regularized variable forgetting factor QRRLS (SR-VFF-QRRLS) algorithm is also proposed. By approximating the covariance matrix in the RLS, new variable regularized and variable step-size transform domain normalized least mean square (VR-TDNLMS and VSS-TDNLMS) algorithms are proposed. Convergence behaviors of these algorithms are studied to characterize their performance and provide useful guidelines for selecting appropriate parameters in practical applications. Based on the local Bayesian estimation framework for linear model parameters developed previously, the resulting estimate can be utilized for recursive nonstationarity detection. This can be cast under the problem of hypothesis testing, as the hypotheses can be viewed as two competitive models between stationary and nonstationary to be selected. In this dissertation, we develop new regularized and recursive generalized likelihood ratio test (GLRT), Rao’s and Wald tests, which can be implemented recursively in a QRRLS-type adaptive filtering algorithm with low computational complexity. Another issue to be addressed in nonstationarity detection is the selection of various models or model orders. In particular, we derive a recursive method for model order selection from the Bayesian Information Criterion (BIC) based on recursive local estimation. In general, the algorithms proposed in this dissertation have addressed some of the important problems in estimation and detection under the local and recursive Bayesian estimation framework. They are intrinsically connected together and can potentially be utilized for various applications. In this dissertation, their applications to adaptive beamforming, ANC system and speech signal processing, e.g. adaptive frequency estimation and nonstationarity detection, have been studied. For adaptive beamforming, the difficulties in determining the regularization or loading factor have been explored by automatically selecting the regularization parameter. For ANC systems, to combat uncertainties in the secondary path estimation, regularization techniques can be employed. Consequently, a new filtered-x VR-QRRLM (Fx-VR-QRRLM) algorithm is proposed and the theoretical analysis helps to address challenging problems in the design of ANC systems. On the other hand, for ANC systems with online secondary-path modeling, the coupling effect of the ANC controller and the secondary path estimator is thoroughly studied by analyzing the Fx-LMS algorithm. For speech signal processing, new approaches for recursive nonstationarity detection with automatic model order selection are proposed, which provides online time-varying autoregressive (TVAR) parameter estimation and the corresponding stationary intervals with low complexity. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

Thesis (M. Sc.)--University of Adelaide, Dept. of Statistics, 1993? / Includes bibliographical references (leaves 88-90).