Computer-intensive rate estimation, diverging statistics and scanning

Details Computer-intensive rate estimation, diverging statistics and scanning Computer-intensive rate estimation, diverging statistics and scanning

2007-10-26

arxiv.org/abs/0710.5004v1

Annals of Statistics 2007, Vol. 35, No. 4, 1827-1848

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000064 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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