No abstract

In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t-distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimation purpose, we use the modified maximum likelihood method in order to get the so-called modified maximum likelihood estimates that are obtained in a closed form. We show that these estimates are substantially more efficient than least-square estimates. They are also found to be robust to reasonable deviations from the assumed distribution and also many data anomalies such as the presence of outliers in the sample, etc. We further provide test statistics for testing the relevant hypothesis regarding the regression coefficients.

Two improved numerical techiques are employed to compute MLE for the paraıneters of the 3'parameter V eibuU distribution using complete sample data of large sample size and of new minimal functional is defined large-valued inspection points. For the solution of estimates a and optimized by the descent method and the method of conjugate gradients. The result of both techniques are compared. Asymptotic variance-covariance matrix of estimates for the complete sample is inciuded.