Brazilian Journal of Probability and Statistics

Simple tail index estimation for dependent and heterogeneous data with missing values

Ivana Ilić and Vladica M. Veličković

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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.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 1 (2019), 192-203.

Dates
Received: July 2017
Accepted: October 2017
First available in Project Euclid: 14 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1547456493

Digital Object Identifier
doi:10.1214/17-BJPS384

Mathematical Reviews number (MathSciNet)
MR3898727

Zentralblatt MATH identifier
07031069

Keywords
Consistency missing observations extremal dependence regular variation tail indices heavy-tailed distributions

Citation

Ilić, Ivana; Veličković, Vladica M. Simple tail index estimation for dependent and heterogeneous data with missing values. Braz. J. Probab. Stat. 33 (2019), no. 1, 192--203. doi:10.1214/17-BJPS384. https://projecteuclid.org/euclid.bjps/1547456493


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