{"title":"A Large Deviation Approximation for Multivariate Density Functions","authors":"C. Joutard","doi":"10.3103/s1066530719010058","DOIUrl":null,"url":null,"abstract":"We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model. Numerical comparisons are eventually provided for these two examples.","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066530719010058","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model. Numerical comparisons are eventually provided for these two examples.
期刊介绍：
Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.
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