Sharp adaptive drift estimation for ergodic diffusions: The multivariate case

Claudia Strauch

Stochastic Processes and their Applications, 2015, vol. 125, issue 7, 2562-2602

Abstract: We consider estimation of the drift function for a large class of multidimensional ergodic diffusions and establish the exact constant of the risk asymptotics in the L2 risk. The constant is of Pinsker-type and in particular reflects the dependence of the drift estimation problem on the geometry of the diffusion coefficient. In addition, an exact data-driven estimation procedure is proposed, attaining the optimal constant under natural L2 Sobolev smoothness conditions on the drift.

Keywords: Ergodic diffusion; Minimax drift estimation; Pinsker’s constant; Sharp minimax adaptivity (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2015.02.003

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