We consider the problem of estimating the integral of the square of a density from the observation of a sample. Our method to estimate 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 -statistics of order 2 due to Houdré and Reynaud.
We consider the problem of estimating the integral of the square of a density
from the observation of a sample. Our method to estimate is
based on model selection 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 -statistics of order 2 due to Houdré and Reynaud.
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 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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