A Randomly Weighting Approximation Approach For Two-tailed Censored Regression Model

In practical application,due to the accuracy of measurement methods and/or tools,when the response variable is greater than the maximum value or less than the minimum value,we can not observe the true value of the response variable.Under this situation,Tobit regression models are often applied to analyze this kind of data.In this paper,the randomly weighted approximation method in the two-tailed Tobit model is studied.We build randomly weighted estimator(RWE)of parameter,and obtain statistical properties of RWE,such as consistency and asymptotic distribution.Based on the above results,we can approximate the distribution of LAD estimators of regression parameters by the conditional distribution of RWE,while it avoids estimating the nuisance parameters,such as the density function of the error term.In addition,we also present an M-test statistic and randomly weighted M test statistic(RWM)to test the linear assumption of the parameters and study the statistical properties of the test statistics.Numerical simulation and real example show that the randomly weighted approximation method performs well.