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Strauch, Claudia

Adaptive invariant density estimation for ergodic diffusions over anisotropic classes. (English) Zbl 1454.62249

Ann. Stat. 46, No. 6B, 3451-3480 (2018).
Summary: Consider some multivariate diffusion process \(\mathbf{X}=(X_{t})_{t\geq0}\) with unique invariant probability measure and associated invariant density \(\rho\), and assume that a continuous record of observations \(X^{T}=(X_{t})_{0\leq t \leq T}\) of \(\mathbf{X}\) is available. Recent results on functional inequalities for symmetric Markov semigroups are used in the statistical analysis of kernel estimators \(\widehat{\rho}_{T}=\widehat{\rho}_{T}(X^{T})\) of \(\rho\). For the basic problem of estimation with respect to sup-norm risk under anisotropic Hölder smoothness constraints, the proposed approach yields an adaptive estimator which converges at a substantially faster rate than in standard multivariate density estimation from i.i.d. observations.

Cited in 2 Reviews
Cited in 19 Documents

MSC:

62M05 Markov processes: estimation; hidden Markov models
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

ergodic diffusion; anisotropic density estimation; adaptation
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Full Text: DOI Euclid

References:

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