On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals

By Evarist Gin'e, Armelle Guillou. 2001

130 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/273405f621d2bd1f8e153ece55d9c4f72ddae101

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Citations in the corpus

Rates of strong uniform consistency for multivariate kernel density estimators (2002, methodology): “1 (Talagrand [15,16]; in this form, Giné and Guillou [7]).”
Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data (2006, background): “2 in Giné and Guillou (2001)] with λ √ n−1 log n, where D is a positive constant, we have”
Generalization bounds for deep convolutional neural networks (2019, methodology): “…enough n ∈ N , for any δ > 0 , for any probability distribution P over Z , if S is obtained by sampling n times independently from P , then, with probability at least 1 − δ , for all g ∈ G , We will also use the following, which is the combination of (2.5) and (2.7) of (Giné and Guillou, 2001).”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, background): “Special cases of the inequalities discussed in Section 3.4 can be found in Talagrand [131], Einmahl and Mason [58], Giné and Guillou [62], Mendelson [108], Giné, Koltchinskii and Wellner [63].”
An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation (2009, background): “This was extended to VC classes of functions by several authors ([11,13,15], among others).”
Uniform in bandwidth consistency of kernel-type function estimators (2005, methodology): “A bound similar to that given in Corollary 4 has been given by Giné and Guillou [13] using a different method.”
Gaussian approximation of suprema of empirical processes (2012, background): “For example, the following corollary is an extension of [26], Proposition 2.”
Asymptotics for panel quantile regression models with individual effects (2012, methodology): “The next proposition is a moment inequality for centered empirical processes, which is due to Proposition 2.2 of Gine and Guillou (2001).”
Size-free generalization bounds for convolutional neural networks (2019, methodology): “We will prove Theorem 3.1 by using || · ||N to witness the fact that `Fβ,ν is ( χλβeνL+β ,W ) -Lipschitz parameterized.”
Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections (2008, background): “As is the case of Bernstein’s inequality in R, Talagrand’s inequality is especially useful in the Gaussian tail range and, combining (15) and (18), one can obtain such a ‘Gaussian tail’ bound for the supremum of the empirical process that depends only on σ (similar to a bound in [10]).”
On Measuring Excess Capacity in Neural Networks (2022, background): “(27) are proven via an asymptotic bound from Giné and Guillou [13], the constant C and the minimal sample size n required for Eq.”
Smoothed quantile regression for panel data (2015, unknown): “The proof is based on the proof of Gine and Guillou (2001, Proposition 2.1), but some modifications are needed. Recall that Ξ̃k, k = 1, . . . , r are i.i.d. Let 1, . . . , r be i.i.d. Rademacher random variables independent of Ξ̃1, . . . , Ξ̃r. By Lemma 2.3.1 of van der Vaart and Wellner (1996), we ”
On local U-statistic processes and the estimation of densities of functions of several sample variables (2007, methodology): “Among them include tight bounds for the absolute moment of the supremum of the [/-statistic process under a uniform covering number bound generalizing a similar bound obtained by Einmahl and Mason [13] and Gine and Koltchin skii [17] (see also Gine and Guillou [16]) for the usual empirical process.”
Rejoinder: Local Rademacher complexities and oracle inequalities in risk minimization (2006, background): “4) The proofs of these types of bounds can be found in [17, 18, 20, 37, 41]; the current version of (2.”