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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....
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...
This paper is devoted to the study of some asymptotic properties of a -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 -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild,...
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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