Variable Selection With Controlling False Discovery Rate Directly In High-dimensions

With the deepening of statistical modeling into every aspect of social life, the dimension of the variable selection problems may be very high. In order to deal with high dimensional data, some penalized methods for variable selection and parame-ter estimation statisticians have been proposed, such as LASSO, MCP and SCAD. Although these penalized methods have an asymptotic oracle property under cer-tain conditions, they do not provide a computable error assessment of the selection results. In this thesis, we study the issue of variable selection with controlling false discovery rate directly in high-dimensions, and propose a so-called Semi-MCP method which can be used in variable selection. Our basic idea is:firstly, select one set of variables S in terms of the MCP penalized criterion; secondly, add the jth selected variable to the candidate model S and consider the hypothesis testing problems in the new candidate model S∪j:finally, evaluate the error of selection results and construct confidence intervals for selected coefficients. We also prove that the Semi-MCP estimation is asymptotic idealness and stickiness under certain conditions. Our simulation studies suggest that the Semi-MCP method is one better method for high-dimensional statistics.