Estimation of the Derivative of a Density and a Related Regression Curve.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let Y1,...,Yn,Y1Y2...Yn be the order statistics of a random sample from a distribution F with density f on the real line. This paper gives a class of estimators of the derivative fx of the density f at points x for which f has a continuous second derivative. These estimators are based on spacings in the order statistics Yjkn - Yj, j 1,...,n-kn, knn, and are shown to be consistent under suitably given conditions. These estimators are then used to estimate a related regression curve in a manner similar to Nadaraya Theory Prob. Appl., 10, 1963, pp. 186-190.
- Statistics and Probability