Open Access
April 1996 Efficient estimation of integral functionals of a density
Béatrice Laurent
Ann. Statist. 24(2): 659-681 (April 1996). DOI: 10.1214/aos/1032894458


We consider the problem of estimating a functional of a density of the type $\int \phi (f, \cdot)$. Starting from efficient estimators of linear and quadratic functionals of f and using a Taylor expansion of $\phi$, we build estimators that achieve the $n^{-1/2}$ rate whenever f is smooth enough. Moreover, we show that these estimators are efficient. Concerning the estimation of quadratic functionals (more precisely, of integrated squared density) Bickel and Ritov have already built efficient estimators. We propose here an alternative construction based on projections, which seems more natural.


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Béatrice Laurent. "Efficient estimation of integral functionals of a density." Ann. Statist. 24 (2) 659 - 681, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0859.62038
MathSciNet: MR1394981
Digital Object Identifier: 10.1214/aos/1032894458

Primary: 62G06 , 62G07 , 62G20

Keywords: Estimation of density , Fourier series , kernel estimators , projection methods , semiparametric Cramér-Rao bound

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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