We investigate least squares estimation for regression coefficients of the covariates in the multiple linear regression model with truncated data and propose an alternative consistent least squares type estimator to the existing ones. The estimator is proved to have an asymptotic normal distribution with the same asymptotic variance matrix as the estimator proposed by Lai and Ying (1992b). However, the estimator is much simpler in computation than Lai and Ying's estimator. The estimation procedure does not require calculation of the nonparametric estimate of the error distribution. A simulation study shows that the estimator performs well even with a moderate sample size.
Tsai, Wei Yann; Liu, Xinhua; and Luo, Xiaodong, "A Least Squares Estimation in Truncated Linear Regression" (March 2007). Columbia University Biostatistics Technical Report Series. Working Paper 8.