Large sample properties of maximum entropy histograms

The large sample properties of a new class of histogram estimators whose derivation is based on an information theory criterion--the maximum entropy principle, which preserves the observed mass and mean--are studied. The pointwise strong consistency, the point-wise asymptotic normality, and the rate of convergence to normality are investigated. The asymptotic mean square error (MSE) of these estimates is also compared relative to the histogram based on spacings, the classical
k
-nearest neighbor, the kernel estimator, and the generalized
k
-nearest neighbor density estimator.