Template-Type: ReDIF-Paper 1.0
Author-Name:  Dorival Leão
Author-Name-First: Dorival
Author-Name-Last: Leão
Author-Name:  Alberto Ohashi
Author-Name-First: Alberto
Author-Name-Last: Ohashi
Title: On the Discrete Cramér-von Mises Statistics under Random Censorship
Abstract:  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 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.
Length:  35 pages
Creation-Date:  2012
File-URL: https://repositorio.insper.edu.br/handle/11224/5914
File-URL: https://repositorio.insper.edu.br/handle/11224/5914
File-Format: text/html
File-Function: Full text
Number: 167
Handle: RePEc:aap:wpaper:167