Sharp adaptive estimation of the drift function for ergodic diffusions

DOI10.1214/009053605000000615zbMATH Open1084.62079arXivmath/0602659OpenAlexW4297810530MaRDI QIDQ817979

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Publication date: 23 March 2006

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Abstract: The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $kgeq1$, but the value of $k$ is not known to the statistician. A fully data-driven procedure of estimating the drift function is proposed, using the estimated risk minimization method. The sharp adaptivity of this procedure is proven up to an optimal constant, when the quality of the estimation is measured by the integrated squared error weighted by the square of the invariant density.

Full work available at URL: https://arxiv.org/abs/math/0602659

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