Almost sure L1-norm convergence for data-based histogram density estimates

The main result of this paper is summarized in Theorem 1, which states that when certain conditions of a general nature are satisfied, the data-based histogram density estimator is strongly consistent in the sence that the mean absolute derivation of the estimator and the density function converges to zero almost surely for any density function, as the sample size increases to infinity.Data-based density estimator histogram