On local U-statistic processes and the estimation of densities of functions of several sample variables
By Evarist Gin'e, David Mason. 2007
89 citations recorded by the source corpus.
A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 517-525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the Lp norms are obtained for these estimators.
Subfields: Artificial Intelligence, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a383e1159f644d4fd6371afe9f2b39daca3d0a49
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In Artificial Intelligence
- Richard Nickl
- I. Castillo
- Evarist Gin'e
- Kolyan Ray
- Judith Rousseau
- A. van der Vaart
- Subhashis Ghosal
- Botond Szab'o
In Finance
- Richard Nickl
- Evarist Gin'e
- I. Castillo
- Judith Rousseau
- Kolyan Ray
- Bharath K. Sriperumbudur
- Karim Lounici
- Subhashis Ghosal
In Statistics and Probability
- Richard Nickl
- I. Castillo
- Kolyan Ray
- Evarist Gin'e
- Judith Rousseau
- D. Chetverikov
- Bharath K. Sriperumbudur
- Kengo Kato
Citations in the corpus
- Nonparametric Bernstein–von Mises theorems in Gaussian white noise (2012, background): “The related problem in density estimation was studied in the papers [15, 20, 30, 31, 33], where it is shown that f ∗ f can be estimated at the 1/√n-rate even when this is impossible for f .”
- Donsker-type theorems for nonparametric maximum likelihood estimators (2007, result): “Similar results have recently been obtained by [13,30] for kernel density estimators.”
- Adaptation on the space of finite signed measures (2008, background): “In the case {ĥn < hp} we have the following: If hp = hmin, then {ĥn < hp} cannot occur, so (7) is proved if t = 0 and will follow from (8) in case t > 0, which we assume for the rest of the proof.”
- Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, methodology): “To apply Talagrand’s inequality we need a bound on the moment of the supremum of the empirical process involved, provided in the following lemma, known for the cases r =∞ (see [14, 17, 25]) and, implicitly, 1≤ r ≤ 2 (see [15]).”