On a Histogram Method of Density Estimation

摘要

Let Y1, Y2,..., Yn, (Y1 = or 1, j=1,..., n-k, are proposed and studied. The estimates are shown to be both weakly and strongly consistent at all ponts x (epsilon)C(f), the continuity set of f, under suitable conditions. Asymptotic distributions of the estimates are given for differing sets of assumptions. Comparisons and efficiencies relative to the kernel type methods of Rosenblatt and Parzen and the histogram method of Revesz are examined. (Author)