Bayesian Technique to Perform the Prediction Process for a Multivariate Mixed Compact Regression Model

Abstract

The matrix-variate extension hyperbola distribution (m-vehd) belongs to the family of probability distributions with heavy tails. It is considered a mixed continuous probability distribution and a twisted probability distribution. It results from mixing the matrix-variate Gaussian variance-mean mixture distribution with the generalized inverse normal distribution (gind). And this distribution has wide applications in the field of economics. On this basis, the paper will study a multivariate compact regression model that follows a(m-vehd).

       Assuming that the shape parameters, scale matrix, and the twisted matrix are known, the parameters of the multivariate compact regression model will be estimated using the Bayesian technique, depending on informative prior information. In addition, the smoothing parameter is selected by a normal distribution rule (rule of thumb) and the kernel function based on the Gauss kernel function and Quartic kernel function, and then finding Bayesian predictive distributions based on informative prior information and estimating the model parameters under balanced and unbalanced loss functions, and application to real data related by the reality of financial inclusion in Arab countries for the year 2014. The researchers concluded the superiority of the Bayes estimator under the balanced quadratic loss function at weight 0.75 and for the Gauss kernel function. In addition, the predictive distribution of future observations is uncommon, but it is an appropriate distribution.