Journal of Statistical Theory and Applications

Volume 14, Issue 2, June 2015, Pages 204 - 213

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

Authors
S.K. Ghoreishi, A. Mostafavinia
Corresponding Author
S.K. Ghoreishi
Received 20 November 2014, Accepted 5 March 2015, Available Online 30 June 2015.
DOI
10.2991/jsta.2015.14.2.8How to use a DOI?
Keywords
Asymptotic optimality; Heteroscedasticity; Multiple linear regression; Shrinkage estimators; Stein’s unbiased risk estimate(SURE)
Abstract

Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators have efficient asymptotic properties in spite of the fact they involve numerous hyperparameters. In this work, we propose a methodology for estimating the hyperparameters whenever one deals with multi-level heteroscedastic hierarchical normal model with several explanatory variables. we investigate the asymptotic properties of the shrinkage estimators when the shrinkage location hyperparameter lies within a suitable interval based on the sample range of the data. Moreover, we show our methodology performs much better in real data sets compared to available approaches.

Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Statistical Theory and Applications
Volume-Issue
14 - 2
Pages
204 - 213
Publication Date
2015/06/30
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.2015.14.2.8How to use a DOI?
Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - S.K. Ghoreishi
AU  - A. Mostafavinia
PY  - 2015
DA  - 2015/06/30
TI  - Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models
JO  - Journal of Statistical Theory and Applications
SP  - 204
EP  - 213
VL  - 14
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2015.14.2.8
DO  - 10.2991/jsta.2015.14.2.8
ID  - Ghoreishi2015
ER  -