A fine-tuned estimator of a general convergence rate
Politis, Dimitris Nicolas
SourceAustralian and New Zealand Journal of Statistics
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Summary A general rate estimation method based on the in-sample evolution of appropriately chosen diverging/converging statistics has recently been proposed by D.N. Politis [C. R. Acad. Sci. Paris, Ser. I, vol. 335, pp. 279-282, 2002] and T. McElroy & D.N. Politis [Ann. Statist., vol. 35, pp. 1827-1848, 2007]. In this paper, we show how a modification of the original estimators achieves a competitive rate of convergence. The modified estimators require the choice of a tuning parameteran optimal such choice is generally a non-trivial problem in practice. Some discussion to that effect is given, as well as a small simulation study in a heavy-tailed setting. © 2008 Australian Statistical Publishing Association Inc.