Document Type : Research Paper

Authors

• Sarmad Abdulkhaleq Salih ¹
• Emad Hazim Aboudi ²

¹ Statistician at the Nineveh Agriculture Directorate, Mosul, Iraq

² Nineveh Agriculture Directorate, Mosul, Iraq.

Abstract

    The matrix-variate generalized hyperbolic distribution is heavy-tailed mixed continuous skewed probability distribution. This distribution has multi applications in the field of economics, risk management, especially in stock modeling.
This paper includes the estimate of the location matrix  $\theta$  for the multivariate partial linear regression model, which is one of the multivariate semiparametric regression models when the random error follows a matrix-variate generalized hyperbolic distribution in the Bayesian technique depending on non-informative and informative prior information, estimating the location matrix under balanced and unbalanced loss function and the shape parameters ($\lambda ,\psi ,\nu$), skewness matrix ($\delta$), the scale matrix $(\mathrm{\Sigma })$ are known. In addition, estimation the smoothing parameter by a proposed method depending on the rule of thumb, the proposed kernel function depending on the mixed Gaussian kernel. the researchers concluded when non-informative and informative prior information is available that the posterior probability distribution for the location matrix  $\theta$ is a matrix-variate generalized hyperbolic distribution, through the experimental side, it was found that the proposed kernel function is overriding than the Gaussian kernel function in estimate the location matrix and under informative prior information.

Keywords

• Multivariate Partial Linear Regression Model
• Matrix-variate generalized hyperbolic distribution
• Kernel functions
• Smoothing Parameter
• Bayesian technique