The matrix-variate generalized hyperbolic distribution belongs to the family of heavy-tailed mixed
probability distributions and is considered to be one of the continuous skewed probability distributions. This distribution has wide applications in the field of economics, especially in stock modeling.
This paper includes estimation the parameters of the multivariate semi-parametric regression
model represented by the multivariate partial linear regression model when the random error follows the matrix-variate generalized hyperbolic distribution, using the Bayesian method when noninformative prior information is available and under the assumption that the shape parameters and
the skewness matrix are known. In addition, the bandwidth parameter is estimated by a suggested
way based on the normal distribution rule and the proposed kernel function based on the mixed
Gaussian kernel function and studying the findings on the generated data in a way suggested for
the model, comparing the estimators depending on the criterion of the mean sum of squares error.
The two researchers concluded that the proposed kernel function is better than the Gaussian kernel
function in estimate the parameters.