Hypothesis Testing for Non-Normal Multiple Compact Regression Model

Abstract

Generalized multivariate transmuted Bessel distribution belongs to the family of probability distributions with a symmetric heavy tail. It is considered a mixed continuous probability distribution. It is the result of mixing the multivariate Gaussian mixture distribution with the generalized inverse normal distribution. On this basis, the paper will study a multiple compact regression model when the random error follows a generalized multivariate transmuted Bessel distribution.

 Assuming that the shape parameters are known, the parameters of the multiple compact regression model will be estimated using the maximum likelihood method and Bayesian approach depending on non-informative prior information. In addition, the Bayes factor was used as a criterion to test the hypotheses. A Gaussian distribution rule selects the bandwidth parameter and the kernel function based on the Gauss kernel function and quartic kernel function. It estimates the model parameters are under quadratic loss function. The researchers concluded that the posterior probability distribution of  is a multivariate t distribution. Applying the findings to real data related to the jaundice percentage in the blood component as a response variable, red blood cell volume and red blood cell sedimentation as parametric influencing variables, and white and red cells as nonparametric influencing variables, the researchers concluded that when the shape parameters increase, the values ​​of the mean square error criteria of  And the variance parameter decreases.