Abstract: Ying, Jung and Wei (1995) proposed an estimation procedure for the censored median regression model that regresses the median of the survival time, or its transform, on the covariates. The procedure requires solving complicated nonlinear equations and thus can be very difficult to implement in practice, especially when there are multiple covariates. Moreover, the asymptotic covariance matrix of the estimator involves the density of the errors that cannot be estimated reliably. In this paper, we propose a new estimator for the censored median regression model. Our estimation procedure involves solving some convex minimization problems and can be easily implemented through linear programming (Koenker and D'Orey (1987)). In addition, a resampling method is presented for estimating the covariance matrix of the new estimator. Numerical studies indicate the superiority of the finite sample performance of our estimator over that in Ying, Jung and Wei (1995).
Key words and phrases: Censoring, convexity, LAD, resampling.