{"title":"On the Strong Law of Large Numbers for Nonnegative Random Variables. With an Application in Survey Sampling","authors":"Tobias Schoch","doi":"10.17713/AJS.V50I3.631","DOIUrl":null,"url":null,"abstract":"Strong laws of large numbers with arbitrary norming sequences for nonnegative not necessarily independent random variables are obtained. From these results we establish, among other things, stability results for weighted sums of nonnegative random variables. A survey sampling application is provided on strong consistency of the Horvitz--Thompson estimator and the ratio estimator.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"48 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Austrian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17713/AJS.V50I3.631","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Strong laws of large numbers with arbitrary norming sequences for nonnegative not necessarily independent random variables are obtained. From these results we establish, among other things, stability results for weighted sums of nonnegative random variables. A survey sampling application is provided on strong consistency of the Horvitz--Thompson estimator and the ratio estimator.
期刊介绍：
The Austrian Journal of Statistics is an open-access journal (without any fees) with a long history and is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. Austrian Journal of Statistics ISNN number is 1026597X Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews.
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