{"title":"舍入数据的两个样本问题","authors":"Y. Nishiyama","doi":"10.14490/JJSS.39.233","DOIUrl":null,"url":null,"abstract":"This paper deals with the two sample problem for rounded data in the i.i.d. model. It is well known that under the null hypothesis the two sample KolmogorovSmirnov statistic without rounding converges in distribution to the supremum of a standard Brownian bridge. We establish that a natural statistic of the KolmogorovSmirnov type based on the rounded data converges in distribution to the same limit as the full observation case. Our result is based on “Donsker’s theorem for discretized data” given by Nishiyama (2008, J. Japan Statist. Soc.).","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two Sample Problem for Rounded Data\",\"authors\":\"Y. Nishiyama\",\"doi\":\"10.14490/JJSS.39.233\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the two sample problem for rounded data in the i.i.d. model. It is well known that under the null hypothesis the two sample KolmogorovSmirnov statistic without rounding converges in distribution to the supremum of a standard Brownian bridge. We establish that a natural statistic of the KolmogorovSmirnov type based on the rounded data converges in distribution to the same limit as the full observation case. Our result is based on “Donsker’s theorem for discretized data” given by Nishiyama (2008, J. Japan Statist. Soc.).\",\"PeriodicalId\":326924,\"journal\":{\"name\":\"Journal of the Japan Statistical Society. Japanese issue\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Japan Statistical Society. Japanese issue\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14490/JJSS.39.233\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Japan Statistical Society. Japanese issue","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14490/JJSS.39.233","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了i.i.d模型中四舍五入数据的两样本问题。众所周知，在零假设下，不舍入的两个样本KolmogorovSmirnov统计量在分布上收敛于标准布朗桥的极值。我们证明了基于舍入数据的kolmogorov - smirnov型自然统计量在分布上收敛到与完全观测情况相同的极限。我们的结果基于Nishiyama (2008, J. Japan Statist)给出的“离散数据的Donsker定理”。Soc)。
This paper deals with the two sample problem for rounded data in the i.i.d. model. It is well known that under the null hypothesis the two sample KolmogorovSmirnov statistic without rounding converges in distribution to the supremum of a standard Brownian bridge. We establish that a natural statistic of the KolmogorovSmirnov type based on the rounded data converges in distribution to the same limit as the full observation case. Our result is based on “Donsker’s theorem for discretized data” given by Nishiyama (2008, J. Japan Statist. Soc.).
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