Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation

In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.