{"title":"Data-dependent probability matching priors for likelihood ratio and adjusted likelihood ratio statistics","authors":"I. Chang, R. Mukerjee","doi":"10.1080/02331888.2011.587880","DOIUrl":null,"url":null,"abstract":"We consider likelihood ratio statistics based on the usual profile likelihood and the standard adjustments thereof proposed in the literature in the presence of nuisance parameters. The role of data-dependent priors in ensuring approximate frequentist validity of posterior credible regions based on the inversion of these statistics is investigated. Unlike what happens with data-free priors, it is seen that the resulting probability matching conditions readily admit solutions which entail approximate frequentist validity of the highest posterior density region as well.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"47 1","pages":"294 - 305"},"PeriodicalIF":1.0000,"publicationDate":"2013-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/02331888.2011.587880","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 2
Abstract
We consider likelihood ratio statistics based on the usual profile likelihood and the standard adjustments thereof proposed in the literature in the presence of nuisance parameters. The role of data-dependent priors in ensuring approximate frequentist validity of posterior credible regions based on the inversion of these statistics is investigated. Unlike what happens with data-free priors, it is seen that the resulting probability matching conditions readily admit solutions which entail approximate frequentist validity of the highest posterior density region as well.
期刊介绍：
Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.
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