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ESTIMATION OF DENSITY FUNCTIONALS

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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 *theta* of the form
*theta* = \int *phi*(*f*(*x*))*dx*, *phi* 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.

**Source**
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