Stochastic Regression Model with Marginal Extreme Value Distribution and Conditional Normal Distribution

Abstract

In various circumstances of stochastic regression analysis, one deals with a random vector (X, Y), where Y is an outcome of X but not vice-versa. In such situations, X has a non-normal distribution while the conditional distribution of (Y|X=x) may or may not be normal. In this paper, the distribution of X is assumed to be Extreme value distribution (Type I) and the conditional distribution of Y to be normal. Then Modified Maximum Likelihood (MML) estimators are derived. Hypothesis testing procedure is also developed.