| Variable selection in high dimensional data analysis has been widely studied in many scientific areas. For example, in genome-wide association study (GWAS), the goal is to identify important variables (i.e., single nucleotide polymorphisms; SNPs) from a large number of variables that are potentially associated with a target phenotype. Among the large number of SNPs, there are usually only a small proportion of them carry valuable information which we call signals. Identifying signals can help people to find out potential causal factors, provide predictions and better understand the scientific problems. However, many signals are weakly associated with the target response. Identifying the weak signals is challenging in large dimensionality studies.;In this dissertation, we first develop a data-driven variable screening procedure, i.e., adaptive false negative control (AFNC) procedure, for weak signal detection. The AFNC procedure can efficiently eliminate unimportant variables while retain a high proportion of signals under block-structured dependence that is widely observed in genomic data analysis. The proposed AFNC procedure is applied to eQTL data analysis from International Hapmap project as well as the signal detection in human height analysis.;Based on adaptive false negative control (AFNC), we also propose a two-stage method in eQTL study. In the first stage, we give a SNP-wise screening by AFNC to eliminate the SNPs which are not associated with any gene. In the second stage, with SNPs retained by false negative control, we use multiple response regression to model the joint effect of SNPs and account for correlation among gene expression values. |
