Goodness-of-fit Test for the Baseline Hazard Rate

We provide a nonparametric test procedure for the baseline hazard function in the generalized Cox model in presence of fixed given covariates. The test statistic is given by an optimal estimator of the quadratic functional of the same function. Our test procedure attains the rate \(n^{-4\alpha /(4\alpha +1)}\) over Besov classes of functions \(B_{\alpha }^{2,\infty }(L)\), \(\alpha ,L>0\), which is known to be minimax optimal in the context of testing the intensity function of a Poisson processes.