Bayesian Estimation of the Normal Location Model: A Non-Standard Approach

IF 1.4 3区经济学 Q2 ECONOMICS

Oxford Bulletin of Economics and Statistics Pub Date : 2025-03-10 DOI:10.1111/obes.12672

Giuseppe De Luca, Jan R. Magnus, Franco Peracchi

{"title":"Bayesian Estimation of the Normal Location Model: A Non-Standard Approach","authors":"Giuseppe De Luca, Jan R. Magnus, Franco Peracchi","doi":"10.1111/obes.12672","DOIUrl":null,"url":null,"abstract":"We consider the estimation of the location parameter <math>\n <semantics>\n <mrow>\n <mi>θ</mi>\n </mrow>\n <annotation>$$ \\theta $$</annotation>\n </semantics></math> in the normal location model and study the sampling properties of shrinkage estimators derived from a non-standard Bayesian approach that places the prior on a scaled version of <math>\n <semantics>\n <mrow>\n <mi>θ</mi>\n </mrow>\n <annotation>$$ \\theta $$</annotation>\n </semantics></math>, interpreted as the “population <math>\n <semantics>\n <mrow>\n <mi>t</mi>\n </mrow>\n <annotation>$$ t $$</annotation>\n </semantics></math>-ratio.” We show that the finite-sample distribution of these estimators is not centred at <math>\n <semantics>\n <mrow>\n <mi>θ</mi>\n </mrow>\n <annotation>$$ \\theta $$</annotation>\n </semantics></math> and is generally non-normal. In the asymptotic theory, we prove uniform <math>\n <semantics>\n <mrow>\n <msqrt>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msqrt>\n </mrow>\n <annotation>$$ \\sqrt{n} $$</annotation>\n </semantics></math>-consistency of our estimators and obtain their asymptotic distribution under a general moving-parameter setup that includes both the fixed-parameter and the local-parameter settings as special cases.","PeriodicalId":54654,"journal":{"name":"Oxford Bulletin of Economics and Statistics","volume":"87 5","pages":"913-923"},"PeriodicalIF":1.4000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/obes.12672","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Oxford Bulletin of Economics and Statistics","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/obes.12672","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}

引用次数: 0

Abstract

We consider the estimation of the location parameter $θ$ in the normal location model and study the sampling properties of shrinkage estimators derived from a non-standard Bayesian approach that places the prior on a scaled version of $θ$ , interpreted as the “population $t$ -ratio.” We show that the finite-sample distribution of these estimators is not centred at $θ$ and is generally non-normal. In the asymptotic theory, we prove uniform $\sqrt{n}$ -consistency of our estimators and obtain their asymptotic distribution under a general moving-parameter setup that includes both the fixed-parameter and the local-parameter settings as special cases.

Abstract Image

查看原文本刊更多论文

正态位置模型的贝叶斯估计：一种非标准方法

我们考虑了正常位置模型中位置参数θ $$ \theta $$的估计，并研究了由非标准贝叶斯方法导出的收缩估计器的抽样特性，该方法将先验放在θ $$ \theta $$的缩放版本上。解释为“人口t $$ t $$ -比率”。我们证明了这些估计量的有限样本分布不以θ $$ \theta $$为中心，并且通常是非正态分布。在渐近理论中，我们证明了我们的估计量的一致n $$ \sqrt{n} $$ -相合性，并得到了它们在一般移动参数设置下的渐近分布，其中固定参数设置和局部参数设置都是特殊情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Oxford Bulletin of Economics and Statistics 管理科学-统计学与概率论

CiteScore

5.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Whilst the Oxford Bulletin of Economics and Statistics publishes papers in all areas of applied economics, emphasis is placed on the practical importance, theoretical interest and policy-relevance of their substantive results, as well as on the methodology and technical competence of the research. Contributions on the topical issues of economic policy and the testing of currently controversial economic theories are encouraged, as well as more empirical research on both developed and developing countries.