Nonparametric Estimation and Testing the Effect of Covariates in Accelerated Life Time Models Under Censoring

We consider an accelerated life time model where the distribution of the basic life time is not specified and the function psi describing the effect of the covariates has no parametric form. That is, the model is completely nonparametric. In this paper, a procedure for testing whether psi has prespecified parametric form is proposed. The approach is based on a transformation to a regression model and the test statistic is a weighted L(2)-distance between a nonparametric estimator for the regression function from the hypothetical regression. Since the problem is investigated for censored data the derivation of the test procedure requires the study of the asymptotic behavior of nonparametric regression estimators under censoring. A proposal for a Monte Carlo procedure for the realization of the test completes the considerations.