The Asymptotic Properties of Mean-centered Binned Kernel Density Estimator

With the massive data set the kernel density estimator has the deficiency of huge computation time. In this situation, the reduction of the computation time is of crucial interest and hence the development of the binned kernel estimator is required. The general framework for binning rule and the resulting binned kernel estimator have been studied by some authors. In this paper we deal with another kind of binning rule, mean-centered binning, which is not included in the general framework for binning. We investigate the asymptotic properties of the mean-centered binned kernel density estimator. We also do the simulation study for the comparison with simple binned kernel estimator.