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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≧l,j=l,…n−k are proposed and studied. The estimates are shown to be both weakly and strongly consistent at ail points x=C(f), the continuity set of f, under suitable conditions.
John Van Ryzin (Mon,) studied this question.