Abstract: We propose a simple estimation method for regression parameter in a partial linear model when the response variable is subject to random right censorship. It is based on suitably stratifying a Gehan-type extension of the Wilcoxon-Mann-Whitney estimating function. The stratification is rational, flexible and natural. The resulting estimate is shown to be consistent and asymptotically normal, even with the size of each stratum being as small as 2. In some special situations, the estimate is asymptotically as accurate as the analogous estimate with the function of the nonparametric component being completely known, implying that the stratification poses little loss of information. Inference is easily obtained through a resampling scheme which is valid with small or moderate sizes of strata. Both the parameter estimation and the resampling scheme can be carried out by linear programming and are easy to implement numerically. Extensive simulations are carried out and the results show strong support of the theory.
Key words and phrases: Accelerated failure time model, asymptotic normality, consistency, efficiency, linear programming, resampling.