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k-th record estimator of the scale parameter of the α-stable distribution

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Stachura M., Wodecka B.
Statistics in Transition new series
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2022
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vol. 23
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issue 4
203-215
EN
Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.
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Extreme value index of left and right tails for financial time series

75%
Dziubdziela W., Stachura M., Wodecka B., Wyższa Szkoła Handlowa im. Bolesława Markowskiego w Kielcach; Wydział Nauk Technicznych, Uniwersytet Jana Kochanowskiego w Kielcach; Wydział Matematyczno-Przyrodniczy; Instytut Matematyki
Acta Universitatis Lodziensis. Folia Oeconomica
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2011
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vol. 255
PL
Praca dotyczy możliwości identyfikacji stopnia grubości ogonów rozkładu poprzez estymację indeksu ekstremalnego. W tym celu stosowane, i dodatkowo porównywane między sobą. są dwie metody. Jedną z nich jest estymator Pickandsa oparty o k-te statystyki pozycyjne, drugą zaś jest alternatywna metoda zaproponowana przez Berreda oparta o k-te wartości.
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