Bootstrap approximations in model checks for binary data

Consider a binary regression model in which the conditional expectation of a binary variable given an explanatory variable belongs to a parametric family. To check whether a sequence of independent and identically distributed observations belongs to such a parametric family, we use Kolmogorov-Smirnov and Cramer-von Mises type tests based on a marked empirical process introduced by Stute. We propose and study a new resampling scheme for a bootstrap in this setup to approximate critical values for these tests. We also apply this approach to simulated and real data. In the latter case we check some parametric models that are used to analyze right-censored lifetime data under a semiparametric random censorship model.