Abstract: The Buckley-James estimator (BJE) is the most appropriate extension of the least squares estimator (LSE) to the right-censored linear regression model. Lai and Ying (1991) established asymptotic normality of the BJE under a set of regularity conditions. The BJE makes use of the product-limit estimator (PLE). Both the LSE and the PLE are asymptotically normally distributed when underlying distributions are either continuous or discontinuous. It is an interesting question whether the BJE is still asymptotic normal when the underlying distributions are discontinuous. In this paper, we show that the BJE has at least four types of asymptotic distributions under various discontinuity assumptions. In particular, we establish certain conditions under which the BJE does (or does not) have an asymptotic normal distribution.
Key words and phrases: Asymptotic normality, identifiability conditions, linear regression model, right-censorship.