Let Y1, Y2, …, Yn, (Y1 ≦ Y2 ≦ … ≦ Yn) be the order statistics of a random sample from a distribution F with density f on the real line. A class of density estimates of the histogram type based on differences of the form Yj+k - Yj, k ≧ 1, j = 1, … n-k are proposed and studied. The estimates are shown to be both weakly and strongly consistent at all points x ε C(f), the continuity set of f, under suitable conditions.
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