Empirical Bayes Estimation in Multiple Linear Regression with Multivariate Skew-Normal Distribution as Prior

We develop a new empirical Bayes analysis in multiple regression models. In the present work we consider multivariate skew-normal 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.