Computer-intensive rate estimation, diverging statistics and scanning

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statis tics. The proposed rate estimators are based on simple least squares argu ments, and are shown to be accurate in a very general setting without requir ing the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extracting useful subsamples of the data series; the pro posed 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 pa rameter are discussed; a small simulation study complements our theoretical results.

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