Regression with response distributions of Pareto-type

The estimation of the Pareto index in presence of covariate information is discussed. The Pareto index is modelled as a function of the explanatory variables and hence measures the tail heaviness of the conditional distribution of the response variable given this covariate information. The original response data are transformed in order to obtain generalized residuals, possessing a common Pareto-type distribution. An exponential regression model will be developed for these generalized residuals. The parameters of this model are estimated using a pro5le likelihood method. The resulting maximum likelihood estimates of the regression coe7cients can be used for the estimation of extreme quantiles of the conditional distribution of the dependent variable. The methods developed are illustrated with two practical examples. c © 2002 Elsevier Science B.V. All rights reserved.