Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

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/).

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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  -