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.