Inference in a Multivariate Generalized Extreme Value Model-Asymptotic Properties of Two Test Statistics

We are here working with a sample from a multivariate GEV model with shape parameter 0, and, for a general 0 in the real line, the asymptotic properties of Gumbel statistic- which balances the upper and lower range of the sample-and of an analogue of the LMP test statistic of Ho: 9 = 0 versus suitable alternatives, are derived. We also compare asymptotically the power of these statistics for solving statistical choice in a multivariate GEV(O) set-up. (o.s.) of samples of increasing size n-+ oc, of independent, identically distributed (i.i.d.) random variables (r.v.'s) with d.f. F E 9(G0), i.e., d.f.'s F for which there exist sequences of real constants {an}In -(an>0) and {bJ}> 1 and a suitable 0ec-, such that F"(a.z+b")-+G,(z), as n-+oo, and for all z E St. 9(G0) is the domain of attraction for maxima of the d.f. G.(-). Although such limiting result is obtained for m fixed, in applications, when analysing the largest observations available, to infer about the tail of F-insurance (censored top fire losses, Ramachandran, (1975), hydrol- ogy (Peaks Over Threshold data)-the model stands valid for reasonably large values of m, and asymptotic properties of statistics related to the model may be called for. Notice also that such statistical model in extreme value theory, introduced first, in a slightly different context, by Pickands (1975) and worked out by several authors (Gomes, 1978, 1981; Weissman, 1978; Smith 1984) compares favourably with Gumbel classical model only if m is reasonably larger than the number of independent maxima in a classical set-up (see Gomes (1985) for comparison of both models). As in the univariate model, inference techniques in a multivariate GE V model are more easily developed for the particular case 0=0; moreover, many important d.f.'s are in the domain of