Adaptive Estimation of a Quadratic Functional of a Density by Model Selection
نویسندگان
چکیده
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(x)dx 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. Mathematics Subject Classification. 62G05, 62G20, 62J02. Received October 23, 2003. Revised July 16, 2004.
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تاریخ انتشار 2005