Efficient linear estimation problem in the bivariate Kotz distribution under dependence assumptions
Our aim in this article is to obtain efficient estimators of the parameters of the bivariate Kotz type distribution considering a particular matrix-variate joint dependence between the sample random vectors. As the normal law is a particular Kotz type distribution, it seems reasonable, taking into account the known results about the normal law, to search such estimators inside the family of unbiased linear estimators. However, we have proven that it is not possible to obtain efficient linear estimators. Then, we have focused our interest on determining the best unbiased linear estimators in the sense of minimizing the distance to the Cramer-Rao lower bound. The results theoretically obtained are illustrated in a numerical simulation example.
estimation kotz type distribution efficiency property