The first part of the dissertation introduces several new methods for estimating thestructure of graphical models. Firstly, we consider estimating graphical models withdiscrete variables, including nominal variables and ordinal variables. For the nominalvariables, we prove the asymptotic...

Interviewer observations are an important source of auxiliary information in survey research. Interviewers can record observations for all units in a sample, and selected observations may be associated with both key survey variables and response propensity. Survey statisticians use auxiliary...

The cause for the observed trends in prostate cancer mortality is unclear. Several authors have indicated that incorrectly classified causes of death have played a role in recent mortality trends. This dissertation is devoted to analyzing competing risks survival data with a misclassified cause...

The Genome-Wide Association Study (GWAS) is the predominant tool to search for genetic risk variants that contribute to complex human disease. Despite the large number of GWAS findings, variants implicated by GWAS are themselves unlikely to fully explain the heritability of many diseases. In...

In the analysis of bivariate correlated failure time data, it is important to measure the strength of association among the correlated failure times. One commonly used measure is the cross-ratio. In the literature, the functional form of cross-ratio is rather restrictive, often assumed to be...

This dissertation focuses on two topics in semiparametric statistical methods and their applications in medical science: (1) prediction of patients? lifetimes based on their risk profiles; (2) estimation of dynamic exposure effects on survival outcomes. In Chapter II, we develop multiple...

Spatial or spatio-temporal data are frequently encountered in many scientific disciplines. One major challenge in modeling these processes is the high dimensionality of such data; that is, the number of observations is usually enormous. The first part of the dissertation proposes an efficient...

In much of applied statistics variables of interest are measured with error. In particular, regression with covariates that are subject to measurement error requires adjustment to avoid biased estimates and invalid inference. We consider two aspects of this problem. Detection Limits (DL) arise...

This thesis develops methodology and asymptotic analysis for sparse estimators of the covariance matrix and the inverse covariance (concentration) matrix in high-dimensional settings. We propose estimators that are invariant to the ordering of the variables and estimators that exploit variable...

Cluster randomized trials, in which social units are selected as the units ofrandomization, have been increasingly used in the past three decades to evaluatethe effects of intervention. This thesis is devoted to design and analysis of clusterrandomized trials.Regarding design, we introduce a new...