Bias reduction via linear combination of nearest neighbour entropy estimators (Q622770)

Summary: 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 a 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.