University of Macau / Faculty of Social Sciences / Department of Sociology

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, December 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 109-119).

Thesis (Ph. D.)--Duke University, 2007.

Most statistical surveys and data collection studies encounter missing data. A common solution to this problem is to discard observations with missing data while reporting the percentage of missing observations in different output tables. Imputation is a tool used to fill in the missing values. This dissertation introduces the missing data problem as well as traditional imputation methods (e.g. hot deck, mean imputation, regression, Markov Chain Monte Carlo, Expectation-Maximization, etc.). The use of artificial neural networks (ANN), a data mining technique, is proposed as an effective imputation procedure. During ANN imputation, computational effort is minimized while accounting for sample design and imputation uncertainty. The mechanism and use of ANN in imputation for complex survey designs is investigated. Imputation methods are not all equally good, and none are universally good. However, simulation results and applications in this dissertation show that regression, Markov chain Monte Carlo, and ANN yield comparable results. Artificial neural networks could be considered as implicit models that take into account the sample design without making strong parametric assumptions. Artificial neural networks make few assumptions about the data, are asymptotically good and robust to multicollinearity and outliers. Overall, ANN could be time and resources efficient for an experienced user compared to other conventional imputation techniques. / Graduation date: 2005

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 233-237).

published_or_final_version / Medical Sciences / Master / Master of Medical Sciences

Thesis (Ph.D.) - Carleton University, 2005. / Includes bibliographical references (p. 252-258). Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

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.