Displaying similar documents to “Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies”

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Adaptive tests for periodic signal detection with applications to laser vibrometry

Magalie Fromont, Céline Lévy-leduc (2006)

ESAIM: Probability and Statistics

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Initially motivated by a practical issue in target detection laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called which corresponds to the minimal distance between the signal and zero so that the detection...

Adaptive tests of qualitative hypotheses

Yannick Baraud, Sylvie Huet, Béatrice Laurent (2003)

ESAIM: Probability and Statistics

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We propose a test of a qualitative hypothesis on the mean of a n -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 ℝ n which are related to Hölderian balls in functional spaces. We provide a simulation...