The Necessary And Sufficient Conditions For Some Kinds Of Pickands Estimators Asymptotic Normality

Suppose X1,X2,...,Xnbe an i.i.d sequence with common distribution functionF(x),with its order statistics , if there exit constants R and non-degenerent distribution function then G(x) must have one of the following three formswhere a > 0 .The three forms can be repressed as following general formwe called that F is in the domain of attractive of G (x). is extreme value index. Ifthe marginal distribution F(x) is unknown, estimate the the extreme value index is an important part in extreme value theory. The necessary and sufficient conditions of some kinds of Pickands estimators asymptotic to normality had been derived in this paper under some general conditions. Main results are briefly as following. For Pickands estimator with two indexes, following theorem is derivedTheorem 2.2 Under conditions of Theorem 2.1, G = N(A, 2) is equivalentFor Pickands estimator with three indexes, one of the main theorems is Theorem 3.2 Under conditions of theorem 3.1, G = N(0 r2) is equivalent toFor Pickands estimator with three indexes, the following theorem is derived Theorem 4.2 Under the conditions of theorem 4.1, G = W(0, 2) is equivalent toTheorem 4.4 Under the conditions of theorem 4.3, G=N(0, 2) is equivalent to...