Graduation date: 1994

Data in the form of counts or proportions often exhibit more variability than that predicted by a Poisson or binomial distribution. Many different models have been proposed to account for extra-Poisson or extra-binomial variation. A simple model includes a single heterogeneity factor (dispersion parameter) in the variance. Other models that allow the dispersion parameter to vary between groups or according to a continuous covariate also exist but require a more complicated analysis. This thesis is concerned with (1) understanding the consequences of using an oversimplified model for overdispersion, (2) presenting diagnostic tools for detecting the dependence of overdispersion on covariates in regression settings for counts and proportions and (3) presenting diagnostic tools for distinguishing between some commonly used models for overdispersed data. The double exponential family of distributions is used as a foundation for this work. A double binomial or double Poisson density is constructed from a binomial or Poisson density and an additional dispersion parameter. This provides a completely parametric framework for modeling overdispersed counts and proportions. The first issue above is addressed by exploring the properties of maximum likelihood estimates obtained from incorrectly specified likelihoods. The diagnostic tools are based on a score test in the double exponential family. An attractive feature of this test is that it can be computed from the components of the deviance in the standard generalized linear model fit. A graphical display is suggested by the score test. For the normal linear model, which is a special case of the double exponential family, the diagnostics reduce to those for heteroscedasticity presented by Cook and Weisberg (1983). / Graduation date: 1990

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

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2004. / Includes bibliographical references (p. 109-111).

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

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

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

Thesis (M. Phil.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 107-110).