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- W2034177275 abstract "Let $varphi$ be a smooth function of $k + 2$ variables. We shall investigate in this paper the rates of convergence of estimators of $T(f) = intvarphi(f(x), f'(x), ldots, f^{(k)}(x), x) dx$ when $f$ belongs to some class of densities of smoothness $s$. We prove that, when $s geq 2k + frac{1}{4}$, one can define an estimator $hat{T}_n$ of $T(f)$, based on $n$ i.i.d. observations of density $f$ on the real line, which converges at the semiparametric rate $1/ sqrt n$. On the other hand, when $s < 2k + frac{1}{4}, T(f)$ cannot be estimated at a rate faster than $n^{-gamma}$ with $gamma = 4(s - k)/lbrack 4s + 1rbrack$. We shall also provide some extensions to the multidimensional case. Those results extend previous works of Levit, of Bickel and Ritov and of Donoho and Nussbaum on estimation of quadratic functionals." @default.
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- W2034177275 date "1995-02-01" @default.
- W2034177275 modified "2023-10-11" @default.
- W2034177275 title "Estimation of Integral Functionals of a Density" @default.
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- W2034177275 doi "https://doi.org/10.1214/aos/1176324452" @default.
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