A class of tests on the tail index
For the i.i.d. sample with d.f. \(F(x)\) a nonparametric test is proposed for the null hypothesis \(H_m:\;x^m(1-F(x))\geq 1\quad\forall x>x_0\) for some \(x_0>0\) with a given \(m>0\), against the alternative \(K_m:\lim\sup_{x\to\infty} x^m(1-F(x))<1\). The test is based on the empirical d.f. of maxima by subsamples. The asymptotic normality of the test statistics and consistency of the test are demonstrated. The test performance is compared with parametric tests via simulations.
scientific article; zbMATH DE number 1833864