In this thesis, we investigate the model checking problem for parametric regression model with missing response at random and nonignorable missing response. Besides, we also propose a hypothesis-adaptive procedure which is based on the dimension reduction theory. Finally, to extend our methods to missing response situation, we consider the dimension reduction problem with missing response at random. The .rst part of the thesis introduces the model checking for parametric models with response missing at random which is a more general missing mechanism than missing completely at random. Di.erent from existing approaches, two tests have normal distributions as the limiting null distributions no matter whether the inverse probability weight is estimated parametrically or nonparametrically. Thus, p-values can be easily determined. This observation shows that slow convergence rate of non­parametric estimation does not have signi.cant e.ect on the asymptotic behaviours of the tests although it may have impact in .nite sample scenarios. The tests can de­tect the alternatives distinct from the null hypothesis at a nonparametric rate which is an optimal rate for locally smoothing-based methods in this area. Simulation study is carried out to examine the performance of the tests. The tests are also applied to analyze a data set on monozygotic twins for illustration. In the second part of the thesis, we consider model checking for general linear re­gression model with non-ignorable missing response. Based on an exponential tilting model, we .rst propose three estimators for the unknown parameter in the general linear regression model. Three empirical process-based tests are constructed. We discuss the asymptotic properties of the proposed tests under null and local alterna­tive hypothesis with di.erent scenarios. We .nd that these three tests perform the same in the asymptotic sense. Simulation studies are also carried out to assess the performance of our proposed test procedures. In the third part, we revisit traditional local smoothing model checking proce­dures. Noticing that the general nonparametric regression model can be considered as a special multi-index model, we propose an adaptive testing procedure based on the dimension reduction theory. To our surprise, our method can detect local alter­native at faster rate than the traditional optimal rate. The theory indicates that in model checking problem, dimensionality may not have strong impact. Simulations are carried out to examine the performance of our methodology. A real data analysis is conducted for illustration. In the last part, we study the dimension reduction problem with missing response at random. Based on the work in this part, we can extend the adaptive testing pro­cedure introduced in the third part to the missing response situation. When there are many predictors, how to e.ciently impute responses missing at random is an important problem to deal with for regression analysis because this missing mech­anism, unlike missing completely at random, is highly related to high-dimensional predictor vector. In su.cient dimension reduction framework, the fusion-re.nement (FR) method in the literature is a promising approach. To make estimation more accurate and e.cient, two methods are suggested in this paper. Among them, one method uses the observed data to help on missing data generation, and the other one is an ad hoc approach that mainly reduces the dimension in the nonparametric smoothing in data generation. A data-adaptive synthesization of these two methods is also developed. Simulations are conducted to examine their performance and a HIV clinical trial dataset is analysed for illustration. Keywords: Model checking; Inverse probability weight; Non-ignorable missing re­sponse; Adaptive; Central subspace; Dimension reduction; Data-adaptive Synthesiza­tion; Missing recovery; Missing response at random; Multiple imputation.

No description available.

In comparing the means .of two normally distributed populations with unknown variance, two tests very often used are: the two independent sample and the paired sample t tests. There is a possible gain in the power of the significance test by using the paired sample design instead of the two independent samples design.

by Long Mei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 73-77). / Abstracts in English and Chinese. / Acknowledgements --- p.iv / Abstract --- p.v / Table of Contents --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Nonlinear Factor Analysis Model --- p.1 / Chapter 1.2 --- Main Objectives --- p.2 / Chapter 1.2.1 --- Investigation of the performance of the ML approach with MCECM algorithm in NFA model --- p.2 / Chapter 1.2.2 --- Investigation of the Robustness of the ML approach with MCECM algorithm --- p.3 / Chapter 1.3 --- Structure of the Thesis --- p.3 / Chapter 2 --- Theoretical Background of the MCECM Algorithm --- p.5 / Chapter 2.1 --- Introduction of the EM algorithm --- p.5 / Chapter 2.2 --- Monte Carlo integration --- p.7 / Chapter 2.3 --- Markov Chains --- p.7 / Chapter 2.4 --- The Metropolis-Hastings algorithm --- p.8 / Chapter 3 --- Maximum Likelihood Estimation of a Nonlinear Factor Analysis Model --- p.10 / Chapter 3.1 --- MCECM Algorithm --- p.10 / Chapter 3.1.1 --- Motivation of Using MCECM algorithm --- p.11 / Chapter 3.1.2 --- Introduction of the Realization of the MCECM algorithm --- p.12 / Chapter 3.1.3 --- Implementation of the E-step via the MH Algorithm --- p.13 / Chapter 3.1.4 --- Maximization Step --- p.15 / Chapter 3.2 --- Monitoring Convergence of MCECM --- p.17 / Chapter 3.2.1 --- Bridge Sampling Method --- p.17 / Chapter 3.2.2 --- Average Batch Mean Method --- p.18 / Chapter 4 --- Simulation Studies --- p.20 / Chapter 4.1 --- The First Simulation Study with the Normal Distribution --- p.20 / Chapter 4.1.1 --- Model Specification --- p.20 / Chapter 4.1.2 --- The Selection of System Parameters --- p.22 / Chapter 4.1.3 --- Monitoring the Convergence --- p.22 / Chapter 4.1.4 --- Simulation Results for the ML Estimates --- p.25 / Chapter 4.2 --- The Second Simulation Study with the Normal Distribution --- p.34 / Chapter 4.2.1 --- Model Specification --- p.34 / Chapter 4.2.2 --- Monitoring the Convergence --- p.35 / Chapter 4.2.3 --- Simulation Results for the ML Estimates --- p.38 / Chapter 4.3 --- The Third Simulation Study on Robustness --- p.47 / Chapter 4.3.1 --- Model Specification --- p.47 / Chapter 4.3.2 --- Monitoring the Convergence --- p.48 / Chapter 4.3.3 --- Simulation Results for the ML Estimates --- p.51 / Chapter 4.4 --- The Fourth Simulation Study on Robustness --- p.59 / Chapter 4.4.1 --- Model Specification --- p.59 / Chapter 4.4.2 --- Monitoring the Convergence --- p.59 / Chapter 4.4.3 --- Simulation Results for the ML Estimates --- p.62 / Chapter 5 --- Conclusion --- p.71 / Bibliography --- p.73

李晓煦. / Submitted: Jan. 2010. / Thesis (doctoral)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 170-175). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in Chinese and English. / Li Xiaoxu.

University of Macau / Faculty of Science and Technology / Department of Electrical and Electronics Engineering

Much data-based research are characterized by the unavoidable problem of incompleteness as a result of missing or erroneous values. This thesis discusses some of the various strategies and basic issues in statistical data analysis to address the missing data problem, and deals with both the problem of missing covariates and missing outcomes. We restrict our attention to consider methodologies which address a specific missing data pattern, namely monotone missingness. The thesis is divided into two parts. The first part placed a particular emphasis on the so called missing at random (MAR) assumption, but focuses the bulk of attention on multiple imputation techniques. The main aim of this part is to investigate various modelling techniques using application studies, and to specify the most appropriate techniques as well as gain insight into the appropriateness of these techniques for handling incomplete data analysis. This thesis first deals with the problem of missing covariate values to estimate regression parameters under a monotone missing covariate pattern. The study is devoted to a comparison of different imputation techniques, namely markov chain monte carlo (MCMC), regression, propensity score (PS) and last observation carried forward (LOCF). The results from the application study revealed that we have universally best methods to deal with missing covariates when the missing data pattern is monotone. Of the methods explored, the MCMC and regression methods of imputation to estimate regression parameters with monotone missingness were preferable to the PS and LOCF methods. This study is also concerned with comparative analysis of the techniques applied to incomplete Gaussian longitudinal outcome or response data due to random dropout. Three different methods are assessed and investigated, namely multiple imputation (MI), inverse probability weighting (IPW) and direct likelihood analysis. The findings in general favoured MI over IPW in the case of continuous outcomes, even when the MAR mechanism holds. The findings further suggest that the use of MI and direct likelihood techniques lead to accurate and equivalent results as both techniques arrive at the same substantive conclusions. The study also compares and contrasts several statistical methods for analyzing incomplete non-Gaussian longitudinal outcomes when the underlying study is subject to ignorable dropout. The methods considered include weighted generalized estimating equations (WGEE), multiple imputation after generalized estimating equations (MI-GEE) and generalized linear mixed model (GLMM). The current study found that the MI-GEE method was considerably robust, doing better than all the other methods in terms of small and large sample sizes, regardless of the dropout rates. The primary interest of the second part of the thesis falls under the non-ignorable dropout (MNAR) modelling frameworks that rely on sensitivity analysis in modelling incomplete Gaussian longitudinal data. The aim of this part is to deal with non-random dropout by explicitly modelling the assumptions that caused the dropout and incorporated this additional sub-model into the model for the measurement data, and to assess the sensitivity of the modelling assumptions. The study pays attention to the analysis of repeated Gaussian measures subject to potentially non-random dropout in order to study the influence on inference that might be caused in the data by the dropout process. We consider the construction of a particular type of selection model, namely the Diggle-Kenward model as a tool for assessing the sensitivity of a selection model in terms of the modelling assumptions. The major conclusions drawn were that there was evidence in favour of the MAR process rather than an MCAR process in the context of the assumed model. In addition, there was the need to obtain further insight into the data by comparing various sensitivity analysis frameworks. Lastly, two families of models were also compared and contrasted to investigate the potential influence on inference that dropout might have or exert on the dependent measurement data considered, and to deal with incomplete sequences. The models were based on selection and pattern mixture frameworks used for sensitivity analysis to jointly model the distribution of the dropout process and longitudinal measurement process. The results of the sensitivity analysis were in agreement and hence led to similar parameter estimates. Additional confidence in the findings was gained as both models led to similar results for significant effects such as marginal treatment effects. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

In this thesis we develop a theoretical framework for the identification of situations where the equal frequency (EF) or equal variance (EV) subclassification may produce lower bias and/or variance of the estimator. We conduct simulation studies to examine the EF and EV approaches under different types of model misspecification. We apply two weighting schemes in our simulations: equal weights (EW) and inverse variance (IV) weights. Our simulation results indicate that under the quadratic term misspecification, the EF-IV estimator provides the lowest bias and root mean square error as compared to the ordinary least square estimator and other propensity score estimators. Our theorem development demonstrates that if higher variation occurs with larger bias for within subclass treatment effect estimates then the EF-IV estimator has a smaller overall bias than the EF-EW estimator. We show that the EF-IV estimator always has a smaller variance than the EF-EW estimator. We also propose a novel method of subclassification that focuses on creating homogeneous propensity score subclasses to produce an estimator with reduced biased in some circumstances. We feel our research contributes to the field of propensity score adjustments by providing new theorems to compare the overall bias and variance between different propensity score estimators. / Graduation date: 2012

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: P.A. Taylor and John F. MacGregor. Includes bibliographical references. Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: P.A. Taylor and John F. MacGregor. Includes bibliographical references. Also available via World Wide Web.