Estimation and hypothesis testing for a nonnormal bivariate distribution with applications

In numerous situations, one deals with a random vector (X, Y), where Y is a consequence of X but not so much the other way round. Often in such situations, X has a nonnormal distribution while the conditional distribution of Y given X = x may or may not be normal. In this paper, we assume the distribution of X to be the extreme value distribution and the conditional distribution of Y to be normal. We derive the MML (modified maximum likelihood) estimators and show that they are highly efficient. We also develop hypothesis testing procedures.