O INSPER E ESTE REPOSITÓRIO NÃO DETÊM OS DIREITOS DE USO E REPRODUÇÃO DOS CONTEÚDOS AQUI REGISTRADOS. É RESPONSABILIDADE DO USUÁRIO VERIFICAR OS USOS PERMITIDOS NA FONTE ORIGINAL, RESPEITANDO-SE OS DIREITOS DE AUTOR OU EDITORLeão, DorivalOhashi, Alberto Masayoshi Faria2023-07-242023-07-242012https://repositorio.insper.edu.br/handle/11224/5914In 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 infinitely 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 [13] and Andersen et al. [5]. 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 infinite-dimensional which allows us to deal consistently with an infinite 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.34 p.DigitalInglêsworking paperCentral Limit TheoremCram´er-von Mises statisticsNonparametric methodsSurvival analysisBEWP 167/2012