Abstract: Let y=βTx+ε; denote the intrinsic relation between the response y and a covariate vector x, where ε represents an unobservable random variable. A truncated regression model assumes the existence of another (truncation) variable t to that (x, y, t) is observed if and only if t<=y and that nothing is observed if t>y. Tsui, Jewell and Wu (1988) have proposed a bias-corrected method to extend the classical least squares approach to regression analysis with truncated data and have found the method to perform well in an extensive simulation study. To develop an asymptotic theory for this approach, we first introduce a slight modification of their estimator to make it more tractable and then establish the consistency and asymptotic normality of the modification under certain regularity conditions. By making use of the asymptotic normality result, approximate confidence regions for β are also given.
Key words and phrases: Asymptotic normality, bias-corrected estimator, consistency, counting process, linear regression, martingale, product-limit estimator, truncation.