Optimal Shrinkage Estimation of Predictive Densities Under α-Divergences

IF 4.9 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Bayesian Analysis Pub Date : 2021-01-01 DOI:10.1214/21-BA1264

E. George, Gourab Mukherjee, Keisuke Yano

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引用次数: 1

Abstract

We consider the problem of estimating the predictive density in a heteroskedastic Gaussian model under general divergence loss. Based on a conjugate hierarchical set-up, we consider generic classes of shrinkage predictive densities that are governed by location and scale hyper-parameters. For any α-divergence loss, we propose a risk-estimation based methodology for tuning these shrinkage hyper-parameters. Our proposed predictive density estimators enjoy optimal asymptotic risk properties that are in concordance with the optimal shrinkage calibration point estimation results established by Xie, Kou, and Brown (2012) for heteroskedastic hierarchical models. These α-divergence risk optimality properties of our proposed predictors are not shared by empirical Bayes predictive density estimators that are calibrated by traditional methods such as maximum likelihood and method of moments. We conduct several numerical studies to compare the non-asymptotic performance of our proposed predictive density estimators with other competing methods and obtain encouraging results. MSC2020 subject classifications: Primary 62L20; secondary 60F15, 60G42.

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α-散度下预测密度的最优收缩估计

我们考虑了一般发散损失下异方差高斯模型中预测密度的估计问题。基于共轭层次结构，我们考虑了由位置和尺度超参数控制的收缩预测密度的一般类别。对于任何α-发散损失，我们提出了一种基于风险估计的方法来调整这些收缩超参数。我们提出的预测密度估计量具有最优渐近风险性质，与Xie、Kou和Brown（2012）为异方差层次模型建立的最优收缩校准点估计结果一致。我们提出的预测因子的这些α-散度风险最优性性质与通过传统方法（如最大似然法和矩量法）校准的经验贝叶斯预测密度估计量不相同。我们进行了几项数值研究，将我们提出的预测密度估计量的非渐近性能与其他竞争方法进行了比较，并获得了令人鼓舞的结果。MSC2020受试者分类：初级62L20；次级60F15、60G42。

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来源期刊

Bayesian Analysis 数学-数学跨学科应用

CiteScore

6.50

自引率

13.60%

发文量

审稿时长

>12 weeks

期刊介绍： Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.