Statistics and Probability Commons^™

Bayesian Flexible Modeling Of Interval-Censored Failure Time Data, Sheng-Yang Wang

Theses and Dissertations

Interval-censored data are a special type of survival data, in which the survival time is not accurately observed but known to fall within a specific time interval. Interval censored data commonly arise in real-life epidemiological and medical studies that involve periodic examinations. In this dissertation, several semi-parametric regression models are investigated to provide flexible modeling and robust inference for interval censored data from Bayesian perspectives.

Chapter 1 provides a detailed description about interval-censored data and gives several examples. Existing models and methods for analyzing such interval-censored data are reviewed as well. Chapter 2 develops a unified Bayesian estimation approach under …

Semiparametric Estimation And Inference In Causal Inference And Measurement Error Models, Jianxuan Liu

Theses and Dissertations

This dissertation research has focused on theoretical and practical developments of semiparametric modeling and statistical inference for high dimensional data and measurement error data. In causal inference framework, when evaluating the effectiveness of medical treatments or social intervention policies, the average treatment effect becomes fundamentally important. We focus on propensity score modelling in treatment effect problems and develop new robust tools to overcome the curse of dimensionality. Furthermore, estimating and testing the effect of covariates of interest while accommodating many other covariates is an important problem in many scientific practices, including but not limited to empirical economics, public health and …

Functional Data Smoothing Methods And Their Applications, Songqiao Huang

Theses and Dissertations

In many subjects such as psychology, geography, physiology or behavioral science, researchers collect and analyze non-traditional data, i.e., data that do not consist of a set of scalar or vector observations, but rather a set of sequential observations measured over a fine grid on a continuous domain, such as time, space, etc. Because the underlying functional structure of the individual datum is of interest, Ramsay and Dalzell (1991) named the collection of topics involving analyzing these functional observations functional data analysis (FDA). Topics in functional data analysis include data smoothing, data registration, regression analysis with functional responses, cluster analysis on …

Improved Simultaneous Estimation Of Location And System Reliability Via Shrinkage Ideas, Beidi Qiang

Theses and Dissertations

In decision theory, when several parameters need to be estimated simultaneously, many standard estimators can be improved, in terms of a combined loss function. The problem of finding such estimators has been well studied in the literature, but mostly under parametric settings, which is inappropriate for heavy-tailed distributions. In the first part of this dissertation, a robust simultaneous estimator of location is proposed using the shrinkage idea. A nonparametric Bayesian estimator is also discussed as an alternative. The proposed estimators do not assume a specific parametric distribution and they do not require the existence of finite moments. The performance of …

Nonparametric Inference For Orderings And Associations Between Two Random Variables, Chuan-Fa Tang

Theses and Dissertations

Ordering and dependency are two aspects to describe the relationship between two random variables. In this thesis, we choose two hypothesis testing problems to tackle; i.e., a goodness-of-fit test for uniform stochastic ordering and one for positive quadrant dependence. For the test for uniform stochastic ordering, we propose new nonparametric tests based on ordinal dominance curves. We derive the limiting distributions of test statistics and provide the least favorable configuration to determine critical values. Numerical evidence is presented to support our theoretical results, and we apply our methods to a real data set. An extension for random right-censored data is …