Thesis (M.S.)--California Polytechnic State University, 2009. / Mode of access: Internet. Title from PDF title page; viewed on June 4, 2009. Major professor: Daniel J. Biezad. "Presented to the faculty California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree [of] Master of Science in Aerospace Engineering." "May 2009." Includes bibliographical references (p. 110-111). Also available on microfiche.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 130-132). Also available on the World Wide Web.

This thesis is concerned with the theory of fitting models of the form y = Xβ + ε, where some distributional assumptions are made on ε. More specifically, suppose that y[sub=j] = Zβ[sub=j] + ε [sub=j] is a model for a component j (j = 1, 2, ..., k) and that one is interested in estimation and interference theory relating to y[sub=T] = Σ [sup=k; sub=j=1] y[sub=j] = Xβ[sub=T] + ε[sub=T]. The theory of estimation and inference relating to the fitting of y[sub=T] is considered within the general framework of general linear model theory. The consequence of independence and dependence of the y[sub=j] (j = 1, 2, ..., k) for estimation and inference is investigated. It is shown that under the assumption of independence of the y[sub=j], the parameter vector of the total equation can easily be obtained by adding corresponding components of the estimates for the parameters of the component models. Under dependence, however, this additivity property seems to break down. Inference theory under dependence is much less tractable than under independence and depends critically, of course, upon whether y[sub=T] is normal or not. Finally, the theory of additivity is extended to classificatory models encountered in designed experiments. It is shown, however, that additivity does not hold in general in nonlinear models. The problem of additivity does not require new computing subroutines for estimation and inference in general in those cases where it works. / Forestry, Faculty of / Graduate

When the distribution of the errors in a linear regression model departs from normality, the method of least squares seems to yield relatively poor estimates of the coefficients. One alternative approach to least squares which has received a great deal of attention of late is minimum L_p norm estimation. However, the statistical efüciency of a L_p estimator depends greatly on the underlying distribution of errors and on the value of p. Thus, the choice of an appropriate value of p is crucial to the effectiveness of _p estimation. Previous work has shown that L₁ estimation is a robust procedure in the sense that it leads to an estimator which has greater statistical efficiency than the least squares estimator in the presence of outliers, and that L₁ estimators have some- desirable statistical properties asymptotically. This dissertation is mainly concerned with the development of a new algorithm for L₁ estimation and constrained L₁ estimation. The mainstream of computational procedures for L₁ estimation has been the simplex-type algorithms via the linear programming formulation. Other procedures are the reweighted least squares method, and. nonlinear programming technique using the penalty function approach or descent method. A new computational algorithm is proposed which combines the reweighted least squares method and the linear programming approach. We employ a modified Karmarkar algorithm to solve the linear programming problem instead of the simplex method. We prove that the proposed algorithm converges in a finite number of iterations. From our simulation study we demonstrate that our algorithm requires fewer iterations to solve standard problems than are required by the simplex-type methods although the amount of computation per iteration is greater for the proposed algorithm. The proposed algorithm for unconstrained L₁ estimation is extended to the case where the L₁ estimates of the parameters of a linear model satisfy certain linear equality and/or inequality constraints. These two procedures are computationally simple to implement since a weighted least squares scheme is adopted at each iteration. Our results indicate that the proposed L₁ estimation procedure yields very accurate and stable estimates and is efficient even when the problem size is large. / Ph. D.

Statistics / M. Sc. (Statistics)

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Keywords: MCEM algorithm; Gibbs sampler; Multivariate probit model; Multi-group; BIC. / The main purpose of this paper is to develop maximum likelihood and Bayesian approach for the multivariate probit model in several populations. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates and the Gibbs sampler is used to produce the joint Bayesian estimates. To test hypotheses involving constraints among the structural parameters of MP model across groups, we use the method of Bayesian Information Criterion(BIC). The simulation study will be given to certify the accuracy of our algorithm. / Yu, Yin. / "March 2007." / Adviser: Sik Yum Lee. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6054. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 135-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

by Wong Kwok Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 50-52). / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- Taguchi's methodology in design of experiments --- p.3 / Chapter 2.1 --- System design / Chapter 2.2 --- Parameter design / Chapter 2.3 --- Tolerance design / Chapter 3. --- Inverse Gaussian distribution --- p.8 / Chapter 3.1 --- Genesis / Chapter 3.2 --- Probability density function / Chapter 3.3 --- Estimation of parameters / Chapter 3.4 --- Applications / Chapter 4. --- Iterative procedures and Derivation of the GLIM 4 macros --- p.21 / Chapter 4.1 --- Generalized linear models with varying dispersion / Chapter 4.2 --- Mean and dispersion models for inverse Gaussian distribution / Chapter 4.3 --- Devising the GLIM 4 macro / Chapter 4.4 --- Model fitting / Chapter 5. --- Simulation Study --- p.34 / Chapter 5.1 --- Generating random variates from the inverse Gaussian distribution / Chapter 5.2 --- Simulation model / Chapter 5.3 --- Results / Chapter 5.4 --- Discussion / Appendix --- p.46 / References --- p.50

Au Kin-Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 49-54). / Abstracts in English and Chinese. / ACKNOWLEDGEMENTS --- p.2 / TABLE OF CONTENTS --- p.3 / ABSTRACT --- p.4 / INTRODUCTION --- p.6 / Media Choice Theories --- p.7 / Performance Feedback and Media Choice --- p.11 / Research Approach --- p.18 / METHOD --- p.20 / Participants --- p.20 / Design --- p.21 / Manipulations --- p.22 / Dependent Measures --- p.24 / Survey Measures --- p.25 / Procedure --- p.27 / Data Analysis --- p.27 / RESULTS --- p.29 / HLM Analysis --- p.32 / DISCUSSION --- p.39 / Media Preference And Bias --- p.43 / Using HLM in Survey Yielding Two-Level Data Set --- p.45 / LIMITATIONS AND FUTURE DIRECTIONS --- p.46 / CONCLUSION --- p.47 / REFERENCES --- p.49 / FOOTNOTES AND APPENDIX --- p.55 / TABLES AND FIGURES --- p.60