Efficient estimation of integral functionals of a density

By Béatrice Laurent. 1996

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Citations in the corpus

Fast Distribution To Real Regression (2013, background): “Suppose that the projection coeﬃcients a ( P ) = { a α ( P ) } α ∈ Z l are as follows for P ∈ I : See [3, 6] for other analyses with this type of assumption.”
Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization (2008, neutral): “08 53”
Fast Function to Function Regression (2014, methodology): “See [3, 5] for other work using similar Sobolev elipsoid assumptions.”
Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization (2007, unknown): “work [9, 13] as well as the more recent work [3, 4, 12].”
Optimal Structural Nested Models for Optimal Sequential Decisions (2004, methodology): “Laurent, B. (1996). Efficient estimation of integral functionals of a density. Annals of Statistics, 24(2): 659 -681. Laurent, B. and Massart, P. (2000). Adaptive estimation of a quadratic functional by model selection. Annals of Statistics, 28(5): 1302-1338. Murphy, Susan. (2003). Optimal dynamic t”
Efficient multivariate entropy estimation via $k$-nearest neighbour distances (2016, background): “We remark that the level of smoothness we require for efficiency in Theorem 1, namely β > d/2 is more than is needed for the two-stage estimator of Laurent (1996) in the case where f is compactly supported and bounded away from zero on its support, where β > d/4 suffices.”
Empirical estimation of entropy functionals with confidence (2010, background): “These include consistent estimators based on entropic graphs [19, 36], gap estimators [43], nearest neighbor distances [17, 26, 29, 45], kernel density plug-in estimators [1, 11, 3, 18, 4, 16], Edgeworth approximations [21], convex risk minimization [35] and orthogonal projections [25].”
Distribution to Distribution Regression (2013, background): “See (Ingster & Stepanova, 2011; Laurent, 1996) for other analysis with this type of assumption.”
Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “Our assumption γ > 1/2 is stronger than the critical assumption γ ≥ 1/4 needed for 1/√n-estimability of some of these functionals [27], a phenomenon intrinsic to general plug-in procedures.”
Goodness-of-fit testing and quadratic functional estimation from indirect observations (2006, methodology): “For the Cramér–Rao bound, we follow the lines of proof in Laurent [20].”
A simple adaptive estimator of the integrated square of a density (2008, background): “Laurent (2005) considered adaptive estimation of ∫”
Estimating Cosmological Parameters from the Dark Matter Distribution (2016, background): “If the space of input densities, I , is in a Sobolov ellip-soid type space; see (Ingster & Stepanova, 2011; Laurent, 1996; Oliva et al., 2014) for details.”
Nonparametric estimation of the likelihood ratio and divergence functionals (2007, background): “Work on this topic dates back to the 1970s [10], [14]; see also [3], [4], [13] and the references therein.”
On Estimating L 22 Divergence (2014, methodology): “Our estimator is based on a line of work studying the estimation of integral functionals of a density in the nonparametric setting [2, 3, 5, 8, 10].”
On Estimating $L_2^2$ Divergence (2014, methodology): “Our estimator is based on a line of work studying the estimation of integral functionals of a density in the nonparametric setting [5, 10, 8, 3, 2].”
Estimating nonquadratic functionals of a density using Haar wavelets (1996, background): “Furthermore, Laurent 1996 has built efficient estimates for s ) 1r4.”