Asymptotically efficient estimation of the index of regular variation

• 成果类型: Article
• 署名作者: Wei, XY
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1995
• 页码: 2036-2058
• 关键词: Extreme Values; tail; parameters; inference; exponent; sums

摘要

We propose a conditional MLE of the index of regular variation when the functional form of a slowly varying function is assumed known in the tail, and we study its asymptotic properties. We prove asymptotic normality of P-theta(kn), a probability measure whose density is the product of the joint conditional density of the k(n) largest order statistics from F-theta(x) given Z(n - k), the (n - k)th order statistic, and a density of Z(n - k) with parameter theta. Based on this result, we shore that this conditional MLE is asymptotically normal and asymptotically efficient in many senses whenever k(n) is o(n). We also propose an iterative estimator of theta given only partial knowledge of L(theta)(x). This estimator is asymptotically normal, asymptotically unbiased and asymptotically efficient.