We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small probability....
We consider the problem of estimating the density of a determinantal process from the observation of independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when goes to infinity, uniform rates of convergence over classes of densities of interest.
We consider the problem of estimating an unknown regression function
when the design is random with values in . Our estimation
procedure is based on model selection and does not rely on any prior
information on the target function. We start with a collection of
linear functional spaces and build, on a data selected space among
this collection, the least-squares estimator. We study the
performance of an estimator which is obtained by modifying this
least-squares estimator on a set of small...
We consider the problem of estimating a function on for large values of by looking for some best approximation of by composite functions of the form . Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions and statistical frameworks. In particular, we handle the problems of approximating by additive functions, single and multiple index models, artificial neural networks, mixtures of Gaussian...
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 a test of a qualitative hypothesis on the mean of a -gaussian vector. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are non-asymptotic. For testing positivity or monotonicity, we establish separation rates with respect to the euclidean distance, over subsets of which are related to Hölderian balls in functional spaces. We provide a simulation study in order...
We consider the problem of estimating the mean of a Gaussian vector with independent components of common unknown variance . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection of estimators of based on and, with the same data , aim at selecting an estimator among with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to may be unknown. We establish...
We propose a test of a qualitative hypothesis on the mean of a -Gaussian
vector. The testing procedure is available when the variance of the
observations is unknown and does not depend on any prior information on
the alternative. The properties of the test are non-asymptotic. For
testing positivity or monotonicity, we
establish separation rates with respect to the Euclidean distance, over
subsets of which are
related to Hölderian balls in functional
spaces. We provide a simulation study in...
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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