On the Discrete Cramér-von Mises Statistics under Random Censorship

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dc.contributor.authorLeão, Dorival
dc.contributor.authorOhashi, Alberto Masayoshi Faria
dc.coverage.cidadeSão Paulopt_BR
dc.coverage.paisBrasilpt_BR
dc.creatorLeão, Dorival
dc.creatorOhashi, Alberto Masayoshi Faria
dc.date.accessioned2023-07-24T16:24:38Z
dc.date.available2023-07-24T16:24:38Z
dc.date.issued2012
dc.description.abstractIn 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.
dc.description.otherIn 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.pt_BR
dc.format.extent34 p.pt_BR
dc.format.mediumDigitalpt_BR
dc.identifier.issueBEWP 167/2012
dc.identifier.urihttps://repositorio.insper.edu.br/handle/11224/5914
dc.language.isoInglêspt_BR
dc.publisherInsperpt_BR
dc.relation.ispartofseriesInsper Working Paperpt_BR
dc.rights.licenseO 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 EDITORpt_BR
dc.subject.keywordsCentral Limit Theorempt_BR
dc.subject.keywordsCram´er-von Mises statisticspt_BR
dc.subject.keywordsNonparametric methodspt_BR
dc.subject.keywordsSurvival analysispt_BR
dc.titleOn the Discrete Cramér-von Mises Statistics under Random Censorshippt_BR
dc.typeworking paper
dspace.entity.typePublication
local.subject.cnpqCiências Exatas e da Terrapt_BR
local.subject.cnpqCiências Sociais Aplicadaspt_BR
local.typeWorking Paperpt_BR
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