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Weighted maxima and sums of non-stationary random-length sequences in heavy-tailed models

Part of: Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  02 April 2025

Natalia Markovich Open the ORCID record for Natalia Markovich [Opens in a new window]
Natalia Markovich*
Affiliation:
Russian Academy of Sciences
*
*Postal address: V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya str. 65, 117997 Moscow, Russia. Email: nat.markovich@gmail.com
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Abstract

Considering a double-indexed array $(Y_{n,i:\,n\ge 1,i\ge 1})$ of non-negative regularly varying random variables, we study the random-length weighted sums and maxima from its ‘row’ sequences. These sums and maxima may have the same tail and extremal indices (Markovich and Rodionov 2020). The main constraints of the latter results are that there exists a unique series in a scheme of series with the minimum tail index and the tail of the term number is lighter than the tail of the terms. Here, a bounded random number of series are allowed to have the minimum tail index and the tail of the term number may be heavier than the tail of the terms. We derive the tail and extremal indices of the weighted non-stationary random-length sequences under a broader set of conditions than in Markovich and Rodionov (2020). We provide examples of random sequences for which the assumptions are valid. Perspectives in adopting the results in different application areas are formulated.

Keywords

Random maximarandom sumsregularly varying tailextremal indextail index

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G32: Statistics of extreme values; tail inference
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 20
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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