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February 2019 Simple tail index estimation for dependent and heterogeneous data with missing values
Ivana Ilić, Vladica M. Veličković
Braz. J. Probab. Stat. 33(1): 192-203 (February 2019). DOI: 10.1214/17-BJPS384

Abstract

Financial returns are known to be nonnormal and tend to have fat-tailed distribution. Also, the dependence of large values in a stochastic process is an important topic in risk, insurance and finance. In the presence of missing values, we deal with the asymptotic properties of a simple “median” estimator of the tail index based on random variables with the heavy-tailed distribution function and certain dependence among the extremes. Weak consistency and asymptotic normality of the proposed estimator are established. The estimator is a special case of a well-known estimator defined in Bacro and Brito [Statistics & Decisions 3 (1993) 133–143]. The advantage of the estimator is its robustness against deviations and compared to Hill’s, it is less affected by the fluctuations related to the maximum of the sample or by the presence of outliers. Several examples are analyzed in order to support the proofs.

Citation

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Ivana Ilić. Vladica M. Veličković. "Simple tail index estimation for dependent and heterogeneous data with missing values." Braz. J. Probab. Stat. 33 (1) 192 - 203, February 2019. https://doi.org/10.1214/17-BJPS384

Information

Received: 1 July 2017; Accepted: 1 October 2017; Published: February 2019
First available in Project Euclid: 14 January 2019

zbMATH: 07031069
MathSciNet: MR3898727
Digital Object Identifier: 10.1214/17-BJPS384

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 1 • February 2019
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