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Sharp adaptive drift estimation for ergodic diffusions: The multivariate case

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  • Strauch, Claudia

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.

Suggested Citation

  • Strauch, Claudia, 2015. "Sharp adaptive drift estimation for ergodic diffusions: The multivariate case," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2562-2602.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:7:p:2562-2602
    DOI: 10.1016/j.spa.2015.02.003
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    References listed on IDEAS

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    1. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics.
    2. Xiaohong Chen & Lars Peter Hansen & Jose Scheinkman, 2009. "Principal Components and Long Run Implications of Multivariate Diffusions," Cowles Foundation Discussion Papers 1694, Cowles Foundation for Research in Economics, Yale University.
    3. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
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    Cited by:

    1. Dexheimer, Niklas & Strauch, Claudia, 2022. "Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 321-362.
    2. Frank Meulen & Moritz Schauer & Jan Waaij, 2018. "Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 603-628, October.
    3. Comte, Fabienne & Genon-Catalot, Valentine, 2021. "Drift estimation on non compact support for diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 174-207.
    4. Wooyong Lee & Priscilla E. Greenwood & Nancy Heckman & Wolfgang Wefelmeyer, 2017. "Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 237-252, July.

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