{"title":"Gaussian Approximations and Related Questions for the Spacings process","authors":"G. Lo","doi":"10.16929/sbs/2018.100-04-05","DOIUrl":"https://doi.org/10.16929/sbs/2018.100-04-05","url":null,"abstract":"All the available results on the approximation of the k-spacings process to Gaussian processes have only used one approach, that is the Shorack and Pyke's one. Here, it is shown that this approach cannot yield a rate better than $% left( N/log log Nright) ^{-frac{1}{4}}left( log Nright) ^{frac{1}{2}% }$. Strong and weak bounds for that rate are specified both where k is fixed and where $krightarrow +infty $. A Glivenko-Cantelli Theorem is given while Stute's result for the increments of the empirical process based on independent and indentically distributed random variables is extended to the spacings process. One of the Mason-Wellner-Shorack cases is also obtained.","PeriodicalId":321019,"journal":{"name":"A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121709861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}