Rates of strong uniform consistency for multivariate kernel density estimators

By Evarist Gin'e, Armelle Guillou. 2002

318 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b4f11f3a85d9dfa900ab37a780ce6ea89f00c4d9

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In Applied Mathematics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Gaussian approximation of suprema of empirical processes (2012, background): “We note that [46] and especially [27, 28] give general sufficient conditions under which K is VC type.”
Nonparametric modal regression (2014, methodology): “ption (K1) is assumed for the kernel density estimator to have the usual rates for its bias and variance. (K2) is for the uniform bounds on the kernel density estimator; this condition can be found inGine and Guillou (2002);Einmahl and Mason (2005);Chen et al. (2014c). We study three types of error ”
Asymptotic theory for density ridges (2014, background): “Note that similar conditions to (K2) appear in Einmahl and Mason (2000, 2005), Giné and Guillou (2002).”
Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections (2008, result): “For classical kernel estimators, results similar to those that follow were obtained in [5,11,13], and for wavelet estimators based on compactly supported wavelets, this was done in [14].”
Linear-Time Learning on Distributions with Approximate Kernel Embeddings (2015, methodology): “We use a suitable form of kernel density estimation, to obtain a uniform error bound with a rate based on the function C − 1 (Gin´e and Guillou 2002).”
An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation (2009, background): “, [14]) that pK n (h ∗∗(t)) estimates p0, if the latter is known to exist and to have derivatives up to order t > 0, at the”
GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, methodology): “, Nolan and Pollard [34], Einmahl and Mason [13], Giné and Guillou [16]), but this does not seem viable in the deconvolution problem, due to the fact that the bounded variation norm does not possess a nice Fourier-analytical characterization.”
Uniform in bandwidth consistency of kernel-type function estimators (2005, background): “MR1383587 [13] Giné, E. and Guillou, A. (2001).”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, methodology): “It is convenient to observe that the degree of concentration of a kernel-type density estimator around its expectation in Lr depends on r, as can already be seen from comparing the known cases r = 1,∞ in [14, 16] for kernel estimators and [17] for wavelets.”
Smoothed quantile regression for panel data (2015, unknown): “1 (Talagrand (1996); in this form, Gine and Guillou (2002)).”
Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results (2006, methodology): “We conclude with the following theorem, whose proof is a little longer and more involved, but it is based on a methodology that is well known and well described in the literature (see [6] and [7]).”