TY - JOUR
T1 - Multi-Goal Prior Selection
T2 - A Way to Reconcile Bayesian and Classical Approaches for Random Effects Models
AU - Hirose, Masayo Y.
AU - Lahiri, Partha
PY - 2020
Y1 - 2020
N2 - The two-level normal hierarchical model has played an important role in statistical theory and applications. In this article, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the model and the associated empirical best linear unbiased predictor of the random effects. We then discuss a new idea for selecting prior for the hyperparameters. The prior, called a multi-goal prior, produces Bayesian solutions for hyperparmeters and random effects that match (in the higher order asymptotic sense) the corresponding classical solution in linear mixed model with respect to several properties. Moreover, we establish for the first time an analytical equivalence of the posterior variances under the proposed multi-goal prior and the corresponding parametric bootstrap second-order mean squared error estimates in the context of a random effects model.
AB - The two-level normal hierarchical model has played an important role in statistical theory and applications. In this article, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the model and the associated empirical best linear unbiased predictor of the random effects. We then discuss a new idea for selecting prior for the hyperparameters. The prior, called a multi-goal prior, produces Bayesian solutions for hyperparmeters and random effects that match (in the higher order asymptotic sense) the corresponding classical solution in linear mixed model with respect to several properties. Moreover, we establish for the first time an analytical equivalence of the posterior variances under the proposed multi-goal prior and the corresponding parametric bootstrap second-order mean squared error estimates in the context of a random effects model.
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U2 - 10.1080/01621459.2020.1737532
DO - 10.1080/01621459.2020.1737532
M3 - Article
AN - SCOPUS:85082805502
JO - Quarterly Publications of the American Statistical Association
JF - Quarterly Publications of the American Statistical Association
SN - 0162-1459
ER -