ON SINGLE INDEX REGRESSION MODELS FOR MULTIVARIATE SURVIVAL TIMES

Abstract

An extension of rank based partial likelihood method of Cox (1975) for general transformation model was introduced by Doksum (1987), and Chaudhuri, Doksum and Samarov (1997) introduced average derivative quantile regression estimates of parameters in semiparametric single index regression models that generalize transformation models. An important requirement for rank and quantile based methods to be applicable to any such model is an intrinsic monotonicity property of the underlying link function. In this note, we explore certain extensions of such semiparametric single index models for multivariate life time data and the possibility of estimation of index coefficients by average derivative quantile regression techniques. Monotonicity properties of the link functions associated with such models are also investigated.