A LASSO-type Approach to Variable Selection and An Approximation by Randomly Weighting Method for Linear Hypothesis Testing in Censored Regression Model

Abstract

Censored regression (“Tobit”) model is one of important regression models and has been widely used in econometrics. However, studies for variable selection problem in censored regression model are rare at the present references. For censored regression model we propose a LASSO-type approach, diverse penalty L1 constraint method (DPLC), to select variables and estimate the corresponding coefficients. Furthermore, we obtain the asymptotic property of estimate of regression coefficient. In addition, we study the linear hypothesis testing problem in censored regression model and use randomly weighting resampling method to approximate to the null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical value of the test statistic can be obtained by the randomly weighting method without estimating the nuisance parameters. At the same time, we also obtain asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model.