Statistical Inferences on High-Dimensional Cox Regression Models

Abstract

High-dimensional data with many and many covariates are available because of drastic progress in data-collecting technology. Hence statistical analysis of such high-dimensional data has been a very important issue for many years. We can find typical methods such as the Lasso even in textbooks for undergraduate students. In additon, in some areas we usually use ultra-high dimensional data such that p~exp(n^c), where p is the number of covariates, n is the sample size, c is a constant. In this paper, we review important studies on survival time data with (ultra-)high dimensional covariates from a perspective of my own studies on high-dimensional data. We focus on the Cox regression model which is one of the most important models for survival analysis. In addition, we refer to related topics.