The Sufficient And Necessary Conditions For The Domains Of Attraction And Conditional Moment Estimator For The Extreme Index

A Sufficient and Necessary Conditions about D(A) is given in the first part: (1). If F ∈ D (∧) , for any α_m > 0, m > 1,then(2). If there exist some α_m > 0,m > 1,s.t.thenSecondly, the necessary condition about D(Φ_α) is given: if F ∈ D(Φ_α),α > 2, then for 0 ≤ p < α - 2, set μp(t) = E((X - t)^p|X > t), we haveIn the second part,we focus on the conditional moment estimator of the extreme value index γ which is based on the conditional momentwhere m_n^j = , j = 1,2. and the strong and weak consis-tency about the estimator is proved.