The Asymptotic Efficiency of Semiparametric Estimators for Censored Linear Regression Models

Abstract

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantile, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.