A simple adaptive estimator of the integrated square of a density

By Evarist Gin'e, Richard Nickl. 2008

69 citations recorded by the source corpus.

; see, for example, Laurent (1996). They arealso part of constants appearing in the exact expression of the MISE of kernel densityestimators and hence their estimates can be used in optimal bandwidth selection. Bickeland Ritov (1988) constructed an eﬃcient and√R n-consistent kernel-based estimator forf

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c87180564b8cf3c7231a2b588cbc241622748103

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In Statistics and Probability

Citations in the corpus

The influence function of semiparametric estimators (2015, background): “as is well known from Goldstein and Messer (1992). The situation is different for functionals of the empirical distribution where Frechet differentiability is only known to hold under special norms, Dudley (1994).”
On Estimating $L_2^2$ Divergence (2014, methodology): “The same is true under the Sobolev assumption, and this property is exploited by Gine and Nickl in exactly the same way as we do here.”
ALTERNATIVE ASYMPTOTICS AND THE PARTIALLY LINEAR MODEL WITH MANY REGRESSORS (2015, background): “As shown by Giné and Nickl (2008), this estimator is optimal, attaining root-n consistency under weak conditions.”
Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency (2018, background): “, Giné and Nickl (2008) and the references therein), but the stated assumption is suffi cient for our purposes.”
On Estimating L 22 Divergence (2014, background): “We also show that this estimator is minimax optimal.”
The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal (2017, methodology): “levels of smoothness is usually achieved using the Lepski method [39, 22, 45, 44, 27], which is not known to be performing well in general in practice.”
Cross-fitting and fast remainder rates for semiparametric estimation (2017, methodology): “By Theorem 3 of Mukherjee, Newey, and Robins (2017) the bias of conditional on the training sample has order . where .”