Pareto Type Tail Index Regression

Extreme value theory is a branch of statistics and has been widely used in many fields such as finance,insurance,environmental science,etc.The main research object in extreme value theory is extreme value distribution.Tail index is often used to characterize the tail features of extreme value distribution and plays an important role in both theoretical research and practi-cal application.This paper starts from the discussion of the tail index of Pareto type distribution.Firstly,considering the covariates and response variables are all complete,the tail index parame-ters are obtained by the local linear method.Secondly,when the response variables are randomly right-censored and the covariates are complete and the censored variables is assumed following the Pareto-type distribution as well,the tail index is obtained by combining the local censoring weights.In this paper,the proposed estimators in these two cases have good asymptotic proper-ties,which satisfy the consistency and asymptotic normality.Moreover,the stochastic simulation is used to further verify the fitting effect of the estimators.