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Density deconvolution with associated stationary data

Le Thi Hong Thuy, Cao Xuan Phuong (2023)

Applications of Mathematics

We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived....

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

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. In the case...

Detecting abrupt changes in random fields

Antoine Chambaz (2002)

ESAIM: Probability and Statistics

This paper is devoted to the study of some asymptotic properties of a M -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M -estimation method, concentration inequalities, maximal inequalities for dependent random variables and φ -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild,...

Detecting abrupt changes in random fields

Antoine Chambaz (2010)

ESAIM: Probability and Statistics

This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under...

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