Bias reduction via linear combination of nearest neighbour entropy estimators

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.