The Asymptotic Property Of Location Invariant Moment-Type Estimator

In this paper, a new estimator of extreme index.denoted by whereandnamed location invariant moment-type estimator, is proposed, and discusses its strong and weak consistency, asymptotic normality property and the optimal choice of sample fraction in four sections, respectively. Main results are briefly as following:Under the first regular variation condition,we obtain its strong and weak consistency in theoremUnder the second regular variation condition,we obtain its asymptotic normality and its asymptotic normality expansion of its function in theorem 4⁸.When condition B is held,the paper discusses the optimal choice of k₀ in the meaning of Mean Square Error in theorem 9.At last we analyze the good property of the proposed estimator,compared with the location invariant Hill — type and Pickands estimator,so as the comparision of the moment estimator when γ≤ 0 by Adjust Algorithm of Adaptive procedure...