Rank Estimation for Mean Residual Life Transformation Model

Abstract

This paper proposes a new and important class of mean residual life regression model, which is called the mean residual life transformation model.  The link function is assumed to be unknown and increasing in its second argument, but it is permitted to be not differentiable. The mean residual life transformation model encompasses the proportional mean residual life model, the additive mean residual life model, and so on. Under maximum rank correlation estimation, we present the estimation procedures, whose asymptotic and finite sample properties are established. The consistent variance can be estimated by a resampling method via perturbing the $U$ -statistics objective function repeatedly which avoids the usual sandwich choice. Monte Carlo simulations reveal good finite sample performance and the estimators are illustrated with the Oscar data set.