Empirical Estimation for Sparse Double-Heteroscedastic Hierarchical Normal Models

DOI

10.2991/jsta.d.200422.001How to use a DOI?

Keywords

Asymptotic optimality; Heteroscedasticity; Empirical estimators; Sparsity; Stein's unbiased risk estimate (SURE)

Abstract

The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for the data sets which exhibit heteroscedasticity mainly due to the lack of constant means rather than unequal variances, the existing models tend to overestimate the variance of the second level model which in turn will cause substantial bias in the parameter estimates. Therefore, in this study, we develop heteroscedastic hierarchical models, called double-heteroscedastic hierarchical models, that take into account the heterogeneity in the means for the second level of the models, in addition to considering the heterogeneity of variance for the first level of the models. In these models, we assume that the vector of means in the second level is sparse. We derive Stein's unbiased risk estimators (SURE) for the parameters in the model based on data decomposition and study their risk properties both in theory and in numerical experiments under the squared loss. The comparison between our SURE estimator and the classical estimators such as empirical Bayes maximum likelihood estimator (EBMLE) and empirical Bayes moment estimator (EBMOM) is illustrated through a simulation study. Finally, we apply our model to a Baseball data set.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Vida Shantia
AU  - S. K. Ghoreishi
PY  - 2020
DA  - 2020/06/02
TI  - Empirical Estimation for Sparse Double-Heteroscedastic Hierarchical Normal Models
JO  - Journal of Statistical Theory and Applications
SP  - 148
EP  - 161
VL  - 19
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200422.001
DO  - 10.2991/jsta.d.200422.001
ID  - Shantia2020
ER  -