The Annals of Statistics

Computer-intensive rate estimation, diverging statistics and scanning

Tucker McElroy and Dimitris N. Politis

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A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown to be accurate in a very general setting without requiring the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extracting useful subsamples of the data series; the proposed rate estimation method is applied to different scans, and the resulting estimators are then combined to improve accuracy. Applications to heavy tail index estimation as well as to the problem of estimating the long memory parameter are discussed; a small simulation study complements our theoretical results.

Article information

Ann. Statist., Volume 35, Number 4 (2007), 1827-1848.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G32: Statistics of extreme values; tail inference

convergence rate heavy tail index long memory subsampling


McElroy, Tucker; Politis, Dimitris N. Computer-intensive rate estimation, diverging statistics and scanning. Ann. Statist. 35 (2007), no. 4, 1827--1848. doi:10.1214/009053607000000064.

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