Asymptotics for Hazard Regression

In hazard regression (HARE), the logarithm of the conditional hazard function of a survival time given a covariate is modeled by a sum of polynomial splines and their tensor products. Under appropriate conditions, it has been shown that the (nonadaptive) HARE estimate of the conditional log-hazard function possesses an optimal L 2 rate of convergence. The current paper considers the L oo rates of convergence and the distributional properties of HARE estimates of the conditional hazard, cumulative hazard, survival and density functions. In particular, it will be shown that these estimates are asymptotically normal. "This research was supported in part by National Science Foundation Grant DMS9403800 and National Institutes of Health Grant CA61937. tThis research' was supported in part by National Science Foundation Grant DMS9504463. AMS 1991 subject classifications. Primary 62G07j secondary 62G20.