高维数据的惩罚复合分位数回归

In various areas of science, heavy-tailed high-dimensional data are commonly encountered. At this point, the classical least squares regression results will become very poor. This article consider the problem of estimating regression coefficient of the linear model. Considering the application of the composite quantile of punishment to estimate of regression coefficients when the real model number as the sample size spread slowly. Among them part considers the penalty with the non-random weight and the random weight. Under certain conditions show that the coefficient of regression estimate has consistency and asymptotic normality. Finally under a variety of error distribution, compare $CR - Lasso $ with $SCAD $, $R - Lasso $ and $Lasso$, $CR - Lasso$ choice of non-zero coefficient is superior to the other three methods when the error distribution is heavy-tailed.