On the Discrete Cramér-von Mises Statistics under Random Censorship
Código: WPE – 275
In this work, nonparametric log-rank-type statistical tests are introduced in order to verify homogeneity of purely discrete variables subject to arbitrary right-censoring for in nitely many categories. In particular, the Cram er-von Mises test statistics for discrete models under censoring
is established. In order to introduce the test, we develop the weighted log-rank statistics in a general multivariate discrete setup which complements previous fundamental results of Gill  and Andersen et al. . Due to the presence of persistent jumps over the unbounded set of categories, the asymptotic distribution of the test is not distribution-free. The statistical test for a large class of weighted processes is described as a weighted series of independent chi-squared variables whose weights can be consistently estimated. Moreover, the associated limiting covariance operator can be in nite-dimensional which allows us to deal consistently with an in nite survival time typically founded in long-term survival analysis such as cure-rate models. The test is consistent to any alternative hypothesis and, in particular, it allows us to deal with crossing hazard functions. We also provide a simulation study in order to illustrate the theoretical results.