Bias reduction via linear combination of nearest neighbour entropy estimators

Authors:
Alexei Kaltchenko;Nina Timofeeva
Affiliations:
Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada.;Department of Computer Science, Yaroslavl State University, Yaroslavl, 150000, Russia
Venue:
International Journal of Information and Coding Theory
Year:
2009

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Abstract

The problem of entropy estimation of stationary ergodic processes is considered. A new family of entropy estimators is constructed as a linear combination of the nearest neighbour estimators with a new metric. The consistency of the new estimators is established for the broad class of measures. The O (n-b)-efficiency of these estimators is established for symmetric probability measures, where b 0 is a constant and n is the number of observations.