On some estimates based on sample behavior near high level excursions
type: Item
instance of: scholarly article
title: On some estimates based on sample behavior near high level excursions
zbMATH Open document ID: 0791.60024
DOI: 10.1007/BF01192168
author: Tailen Hsing
publication date: 1994-05-18T00:00:00Z
review text: Let \(\{\xi_ j\}\) be a stationary sequence of weakly dependent random variables and let \(M_ n^{(k)}\) be the \(k\)-th largest value of \(\xi_ j\), \(1 \leq j \leq n\). The estimation of the parameters of the asymptotic distribution of \(M_ n^{(k)}\) is considered using a procedure motivated by a limit theorem pertaining to the point process \(\sum_ j \delta_{(j/n,n \overline F(\xi_ j))}\). A number of statistical issues concerning the procedure, including how to select the tuning parameters, are addressed. The second problem that we consider is the estimation of the filter of a moving average process with heavy tails. In particular, the investigation covers the moving average stable process. Motivated by ideas of \textit{H. Rootzén} [Ann. Probab. 6, 847-869 (1978; Zbl 0394.60025)], our estimator uses information contained in the sample behavior of the process near the largest excursion.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 569046
zbMATH Keywords: weakly dependent random variables
zbMATH Keywords: point process
zbMATH Keywords: moving average process
zbMATH Keywords: sample behavior of the process near the largest excursion
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569046