In this paper, we consider a multidimensional convolution model for which we provide adaptive anisotropic kernel estimators of a signal density measured with additive error. For this, we generalize Fan’s (
(3) (1991) 1257–1272) estimators to multidimensional setting and use a bandwidth selection device in the spirit of Goldenshluger and Lepski’s (
(3) (2011) 1608–1632) proposal for density estimation without noise. We consider first the pointwise setting and then,...
In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among...
We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide...
This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive estimator....
In this paper, we study the problem of non parametric estimation
of an unknown regression function from dependent data with
sub-Gaussian errors. As a particular case, we handle the
autoregressive framework. For this purpose, we consider a
collection of finite dimensional linear spaces ( linear spaces
spanned by wavelets or piecewise polynomials on a possibly
irregular grid) and we estimate the regression function by a
least-squares estimator built on a data driven selected linear
space among the...
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