{"title":"UNIFORM STRONG CONVERGENCE OF A GENERALIZED FAILURE RATE ESTIMATE","authors":"I. Ahmad","doi":"10.5109/13105","DOIUrl":null,"url":null,"abstract":"Under certain conditions it is shown that uniform continuity of the generalized failure rate function is necessary and sufficient for strong uniform consistency of a class of estimators based on the kernel estimates of the probability density and distribution functions due to Parzen (1962) and Nadaraya (1970). The result is proved for the univariate generalized failure rate function due to Barlow and Van Zwet (1970) and for its bivariate extension. Our results contain as special cases the work of Schuster (1969) for the univariate densities and Samanta (1973) for the bivariate densities.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1976-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5109/13105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 19
Abstract
Under certain conditions it is shown that uniform continuity of the generalized failure rate function is necessary and sufficient for strong uniform consistency of a class of estimators based on the kernel estimates of the probability density and distribution functions due to Parzen (1962) and Nadaraya (1970). The result is proved for the univariate generalized failure rate function due to Barlow and Van Zwet (1970) and for its bivariate extension. Our results contain as special cases the work of Schuster (1969) for the univariate densities and Samanta (1973) for the bivariate densities.
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