多元密度函数的大偏差近似

IF 0.8 Q3 STATISTICS & PROBABILITY

Mathematical Methods of Statistics Pub Date : 2019-05-03 DOI:10.3103/s1066530719010058

C. Joutard

{"title":"多元密度函数的大偏差近似","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":"{\"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}","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

摘要

通过对归一化累积量生成函数及其导数的若干假设，建立了任意随机向量序列密度的大偏差近似。我们给出了两个统计应用来说明结果，第一个是处理独立样本方差的向量，第二个是高斯多元线性回归模型。最后对这两个例子进行了数值比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A Large Deviation Approximation for Multivariate Density Functions

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

0.00%

发文量

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.