An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation

By Evarist Gin'e, Richard Nickl. 2009

70 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

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Citations in the corpus

On the optimal estimation of probability measures in weak and strong topologies (2013, background): “Several recent works [6, 26, 16, 17, 18, 19] have shown that many popular density estimators on X = R, such as maximum likelihood estimator, kernel density estimator and wavelet estimator satisfy (2) if F is P-Donsker—the Donsker classes that were considered in these works are: functions of bounded ”
Adaptation on the space of finite signed measures (2008, methodology): “The proof of the lemma follows Theorem 1 in Giné and Nickl [9], but requires substantial technical modifications.”
Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections (2008, unknown): “Keywords: adaptive estimation; Lepski’s method; Rademacher processes; spline estimator; sup-norm loss; wavelet estimator”
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, methodology): “ving a Bernstein-von Mises theorem when d≥ 4, and also necessitates the assumption s>a− 1 + d/2 in Theorem 3. Similar phenomena occur in nonparametric smoothing problems, see, e.g., Section 3.6 in [24]. 2.5 CLTs and asymptotic inference for the invariant measure We now turn to the problem of maki”
CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, methodology): “Condition (K5) follows from Lemma 2 in Giné and Nickl (2009b).”
Anti-concentration and honest, adaptive confidence bands (2013, methodology): “Previous literature on the Lepski method used Talagrand’s inequality combined with some bounds on expected suprema of certain empirical processes (obtained via symmetrization and entropy methods) to choose the threshold level for the estimator [the right-hand side of the inequality in (35)]; see [19”
On adaptive inference and confidence bands (2011, background): “About question (ii): if the radius B of the Hölder balls involved is known, then one can combine a natural testing approach with recent results in [10, 11, 13] to prove the existence of adaptive nonparametric confidence bands over a scale of Hölder classes indexed by a grid of smoothness parameters ”
Confidence sets in sparse regression (2012, methodology): “To formalise these ideas, we take the separation approach to adaptive confidence sets introduced in Giné and Nickl (2010), Hoffmann and Nickl (2011), Bull and Nickl (2013) in the framework of nonparametric function estimation.”