Empirical Bayes Estimation in Multiple Linear Regression with Multivariate Skew-Normal Distribution as Prior
Abstract
We develop a new empirical Bayes analysis in multiple
regression models. In the present work we consider multivariate skewnormal
as prior for coefficients of the model in a skew-normal population
and give empirical Bayes estimation for parameters of the model. The
marginal distribution of response is found to be a closed skew-normal
distribution. The empirical Bayes estimator is found in a closed form
and the model is applied on a data set.
regression models. In the present work we consider multivariate skewnormal
as prior for coefficients of the model in a skew-normal population
and give empirical Bayes estimation for parameters of the model. The
marginal distribution of response is found to be a closed skew-normal
distribution. The empirical Bayes estimator is found in a closed form
and the model is applied on a data set.
Keywords
Multivariate skew-normal distribution, multivariate
closed skew-normal distribution; empirical bayes estimation;
bayesian regression.
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