ESTIMATION OF COEFFICIENTS AND SCALE PARAMETER FOR LINEAR (TYPE 1) EXTREME VALUE REGRESSION MODEL FOR LARGEST VALUES WITH APPLICATIONS

Abstract

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients , goodness of fit statistics based on the observed residuals are considered . As a conclusion and  through the probability plot test we get no evidence against using the assumed residuals distribution.