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December 1995 Asymptotically efficient estimation of the index of regular variation
Xiaoying Wei
Ann. Statist. 23(6): 2036-2058 (December 1995). DOI: 10.1214/aos/1034713646


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 $P_{\theta}^{k_n}$, 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 show 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.


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Xiaoying Wei. "Asymptotically efficient estimation of the index of regular variation." Ann. Statist. 23 (6) 2036 - 2058, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0854.62022
MathSciNet: MR1389864
Digital Object Identifier: 10.1214/aos/1034713646

Primary: 62F12
Secondary: 62G20

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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