Approximation by randomly weighting method in censored regression model  

作　　者：WANG ZhanFeng WU YaoHua ZHAO LinCheng 

机构地区：[1]Department of Statistics and Finance,University of Science and Technology of China,Hefei 230026,China

出　　处：《Science China Mathematics》2009年第3期561-576,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10471136);PhD Program Foundation of the Ministry of Education of China;Special Foundations of the Chinese Academy of Sciences and University of Science and Technology of China

摘　　要：Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.Censored regression (“Tobit”) models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.

关 键 词：censored regression model least absolute deviation asymptotic normality local alternative randomly weighting method asymptotic power 62G10 62G20 62G05 

分 类 号：O212.1[理学—概率论与数理统计]