Open Access
August 2007 Computer-intensive rate estimation, diverging statistics and scanning
Tucker McElroy, Dimitris N. Politis
Ann. Statist. 35(4): 1827-1848 (August 2007). DOI: 10.1214/009053607000000064


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.


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Tucker McElroy. Dimitris N. Politis. "Computer-intensive rate estimation, diverging statistics and scanning." Ann. Statist. 35 (4) 1827 - 1848, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1209.62050
MathSciNet: MR2351107
Digital Object Identifier: 10.1214/009053607000000064

Primary: 62G05 , 62G32

Keywords: convergence rate , heavy tail index , long memory , subsampling

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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