Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

• Published in: Journal of statistical theory and applications Vol. 14; no. 2; pp. 204 - 213
• Main Authors: Ghoreishi, S. K., Mostafavinia, A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2015; Springer Nature B.V; Springer
• Subjects: Asymptotic optimality; Heteroscedasticity; Multiple linear regression; Shrinkage estimators; Stein’s unbiased risk estimate(SURE); Asymptotic properties; Empirical analysis; Estimators; Normality; Research Article; 2000 Mathematics Subject Classification; Shrinkage estimators; Stein’s unbiased risk estimate(SURE); 62F30; Asymptotic optimality; Multiple linear regression; 62F15; Heteroscedasticity
• ISSN: 1538-7887; 2214-1766; 1538-7887
• DOI: 10.2991/jsta.2015.14.2.8

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.