Donsker-type theorems for nonparametric maximum likelihood estimators

By Richard Nickl. 2007

40 citations recorded by the source corpus.

Subfields: Artificial Intelligence, 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): “Similar result is shown for wavelet density estimators and spline projection estimators in F = { 1 ( ,t ] : t ∈ R [18, 19] and maximum likelihood estimators in F BL [26].”
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 .”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, background): “our general theorem gives the right rate for Bayesian posteriors if r>2—similar problems are known with nonparametric maximum likelihood estimators in Lr-metrics (cf. the proof of Proposition 6 in [27]). While we do not settle the issue of optimality of our rates for r>2 in this article, we al”
An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation (2009, background): “In the recent articles [2,17,18,29], it was shown that several nonparametric density estimators (such as maximum likelihood, wavelet or kernel estimators) are within a ‖ · ‖F -ball of probabilistic size o(1/√n) around the empirical measure, where ‖μ‖F = sup f ∈F | ∫ f dμ| is the usual supnorm of a m”
Uniform limit theorems for wavelet density estimators (2008, unknown): “Considering the central limit theorem, such results were proved for other density estimators—such as nonparametric maximum likelihood estimators and kernel density estimators—in Nickl (2007) and Giné and Nickl (2008).”
On Bayesian supremum norm contraction rates (2013, methodology): “This work started from ideas developed in the work [6] in common with Richard Nickl.”
Uniform central limit theorems for kernel density estimators (2008, background): “Nickl [18,19] studies UCLTs and the plug-in property for other density estimators, particularly, for nonparametric maximum likelihood estimators, sieved maximum likelihood estimators (for trigonometric sieves), as well as trigonometric series estimators.”