期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2019
卷号：33
期号：1
页码：192-203
DOI：10.1214/17-BJPS384
语种：English
出版社：Brazilian Statistical Association
摘要：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.
