Research On FDR And An Estimate Of Its Paramter In Multiple Testing

With the continual development and progress of the information era, large amount of high-throughput data increasingly emerges, so that the statistical analysis of mega data becomes so important and significant. As one of the main fundamentals in contemporary statistics, multiple testing problems at-tract many attentions. Central and the most important issue to the problems is how to control the overall testing error rate when we simultaneously perform many tests of significance. The traditional error control procedure (FWER) appears to be too conservative. Since Benjamini and Hochberg (1995) pro-posed a new approach, research of multiple testing problems has focused on the false discovery rate (FDR). In this dissertation, various multiple testing procedures based on FDR are studied and developed.The dissertation consists of six chapters that are organized as follows.In Chapter one, we describe the backgrounds of multiple testing problems, introduce the definitions of a variety of overall testing error rate measurements in multiple testing problems, and show their differences and connections. In Chapter 2, we discuss several testing procedures, including improvements of testing over difference method and testing based on Fdr and fdr.Estimation of the proportion of true null hypothesesπ0 is considered in Chapter 3. As the proportion parameter is of great significance for improve-ment of testing procedures, many estimators are proposed by many statisti-cians. In this chapter, we describes several existing estimators, and improve the estimate of difference method. All the estimates are compared through simula-tion studies. We propose parametric mixture models in Chapter 4. Computa-tion algorithms and simulation results are given for normal and beta mixture models, respectively. In Chapter 5, we propose a nonparametric exponential mixture model to fit the p-values. The procedure has the advantages of identi-fiability, flexibility and regularity. The nonparametric MLE is proposed to be approximated by EM algorithm including weighted EM algorithm. Simulation results show that the new estimate is usually smaller with lower biases than the other three conservative estimates.In the last chapter, the new procedure is applied to two sets of real mi-croarray data with comparisons over several methods.