On the ABLUE of the scale parameter of the generalized Pareto distribution

Abstract

We study the asymptotic best linear unbiased estimation of the scale parameter of the generalized Pareto distribution (GPD) with the probability density function (p.d.f.)
$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~&r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),~~&r=0. \end{array}\right.$$
In Cheng and Chou (2000), the best linear unbiased estimation of the scale parameter was discussed for finite samples. We study the large sample size cases here. Results of some chosen cases are tabulated.