We propose a method based on a penalised likelihood criterion, for estimating the number on non-zero components of the mean of a Gaussian vector. Following the work of Birgé and Massart in Gaussian model selection, we choose the penalty function such that the resulting estimator minimises the Kullback risk.
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...
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