Displaying similar documents to “Nonparametric prediction via mode.”

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

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The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found. ...

Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet, Paul Doukhan, Gabriel Lang, Nicolas Ragache (2008)

ESAIM: Probability and Statistics

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In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the...

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2001)

ESAIM: Probability and Statistics

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We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H 0 : “ f = f 0 ” against the composite alternative H a : “ f ≠ f 0 ” under the assumption that the true regression function f is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of f and the function f 0 , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H 0 . We study...

Diffusions with measurement errors. II. Optimal estimators

Arnaud Gloter, Jean Jacod (2001)

ESAIM: Probability and Statistics

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We consider a diffusion process X which is observed at times i / n for i = 0 , 1 , ... , n , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance ρ n . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a gaussian martingale, and we conjecture that they are also optimal in the general case.