THE L(2) RATE OF CONVERGENCE FOR HAZARD REGRESSION

The logarithm of the conditional hazard function of a survival time gi ven one or more covariates is approximated by a function having the fo rm of a specified sum of functions of at most d of the variables. Subj ect to this form, the approximation is chosen to maximize the expected conditional log-likelihood. Maximum likelihood and sums of tenser pro ducts of polynomial splines are used to construct an estimate of this approximation based on a random sample. The components of this estimat e possess a rate of convergence that depends only on d and a suitably defined smoothness parameter.