On predictive density estimation for location families under integrated squared error loss

Tatsuya Kubokawa, Éric Marchand and William E. Strawderman

Journal of Multivariate Analysis, 2015, vol. 142, issue C, 57-74

Abstract: Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated squared error loss. Our findings relate to a d-variate spherically symmetric observable X∼pX(‖x−μ‖2) and the objective of estimating the density of Y∼qY(‖y−μ‖2) based on X. We describe Bayes estimation, minimum risk equivariant estimation (MRE), and minimax estimation. We focus on the risk performance of the benchmark minimum risk equivariant estimator, plug-in estimators, and plug-in type estimators with expanded scale. For the multivariate normal case, we make use of a duality result with a point estimation problem bringing into play reflected normal loss. In three or more dimensions (i.e., d≥3), we show that the MRE predictive density estimator is inadmissible and provide dominating estimators. This brings into play Stein-type results for estimating a multivariate normal mean with a loss which is a concave and increasing function of ‖μˆ−μ‖2. We also study the phenomenon of improvement on the plug-in density estimator of the form qY(‖y−aX‖2),01, showing in some cases, inevitably for large enough d, that all choices c>1 are dominating estimators. Extensions are obtained for scale mixture of normals including a general inadmissibility result of the MRE estimator for d≥3.

Keywords: Concave loss; Convolutions; Dominance; Frequentist risk; Inadmissibility; Integrated squared error; Minimax; Minimum risk equivariant; Loss function; Multivariate normal; Predictive density; Restricted parameter space; Scale mixture of normals; Stein estimation (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X15001840
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:142:y:2015:i:c:p:57-74

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2015.07.013

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().