Asymptotic distribution of a histogram density estimator
B K Kim, John Van Ryzin · University of North Texas Digital Library (University of North Texas) · 1980
Two theorems on the asymptotic distribution of a histogram density estimator based on randomly determined spacings introduced by Van Ryzin in 1973 are stated and proved. One theorem gives conditions for the pointwise asymptotic normality of the density estimator for points in the support of the density at which the density is continuously differentiable. A second theorem gives conditions for the pointwise asymptotic normality of the density estimator with a faster convergence rate for points in the support of the density at which the density is twice continuously differentiable. The results are used to compare the relative asymptotic efficiencies of the histogram estimator with the kernal method of density estimation.