Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea

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Displaying similar documents to “Exact adaptive pointwise estimation on Sobolev classes of densities”

On pointwise adaptive curve estimation based on inhomogeneous data

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ESAIM: Probability and Statistics

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We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists ...

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2004)

ESAIM: Probability and Statistics

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We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2002)

ESAIM: Probability and Statistics

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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 $H_{a}$ : “ $f \neq f_{0}$ ” 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...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density $f$ from the observation of a $n$ sample. Our method to estimate $\int_{ℝ} f^{2} (x) d x$ is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for $U$ -statistics of order 2 due to Houdré and Reynaud.

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

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We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator....

Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau (2008)

ESAIM: Probability and Statistics

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In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided. ...