ESTIMATION OF DENSITY FUNCTIONALS

RUDOLF GRÜBEL

FB 17 (Mathematik-Informatik), Universität-GH Paderborn, 33095 Paderborn, Germany

(Received March 30, 1992; revised February 23, 1993)

Abstract. Given a sequence of independent random variables with density f we estimate quantities θ of the form θ = ∫ ϕ(f(x))dx, ϕ a known function, by inserting histograms and kernel density estimators for the unknown f. We obtain conditions for consistency and asymptotic normality and discuss the choice of cell size and bandwidth.

Key words and phrases: Density functionals, empirical central limit theorem, estimation.