Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

Abstract

From practical point of view, in a two-level hierarchical model, the variance of second-level usually has a tendency to change through sub-populations. The existence of this kind of local (or intrinsic ) heteroscedasticity is a major concern in the application of statistical modeling. The main purpose of this study is to construct a Bayesian methodology via shrinkage priors in order to estimate the interesting parameters under local heteroscedasticity. The suggested methodology for this issue is to use of a class of the local-global shrinkage priors, called Dirichlet-Laplace priors. The optimal posterior concentration and straightforward posterior computation are the appealing properties of these priors. Two real data sets are analyzed to illustrate the proposed methodology.

Restricted Empirical Likelihood Estimation for Time Series Autoregressive Models

“…2. Unlike the usual way, the priors 1 and 2 are dependent of n. This is often assumed in Bayesian statistical analysis; for more details see Bhattacharya et al [26] and Ghoreishi [27]. However, the functions H 1 and H 2 can also be chosen in such a way that the effect of sample size is ignorable.…”

A class of Bivariate SURE estimators in heteroscedastic hierarchical normal models

“…For homoscedastic case, we can refer to Baranchik (1970), Strawderman (1971), Brown (1971Brown ( , 1975 and Berger (1976) among the others, while the heteroscedastic situation have been addressed by a few authors. For more details see Hudson (1974), Xie et al (2012), Ghoreishi andMeshkani (2014, 2015).…”