Random weighting approximation for Tobit regression models with longitudinal data

Longitudinal data arise naturally in medical studies, psychology, sociology and so on. Due to some lower detection limits the responses are often left censored, which are called Tobit responses in econometrics. For Tobit response regression models with longitudinal data, quantile estimators of regression parameters and M-test statistics for linear hypotheses are constructed. In addition, distributions of the proposed estimators and test statistics are formed by random weighting method. The proposed methods do not need to estimate nuisance parameters involved in asymptotic distributions of the developed statistics. Extensive simulations and a real data example are presented to demonstrate the performance of the proposed methods.