Sharp adaptive estimation of the drift function for ergodic diffusions
By Arnak S. Dalalyan. 2005
68 citations recorded by the source corpus.
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift S(·) is supposed to belong to a nonparametric class of smooth functions of order k ≥ 1, 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.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6799344122de8eaf7da957083b836ad49e6fc13e
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In Finance
- Fabienne Comte
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- Kolyan Ray
- Yves Rozenholc
- Richard Nickl
- Christian M. Hafner
- Evarist Gin'e
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In Statistics and Probability
- Kolyan Ray
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- Fabienne Comte
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- Yves Rozenholc
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- Evarist Gin'e
Citations in the corpus
- Penalized nonparametric mean square estimation of the coefficients of diffusion processes (2007, result): “Asymptotic results were given for ergodic models as the length of the observation time interval tends to infinity: see, for instance, the reference paper by Banon [2], followed by more recent works by Prakasa Rao [30], Spokoiny [31], Kutoyants [28] or Dalalyan [18].”
- Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, background): “, [30], [14, 15, 50, 38, 54, 1, 2, 3]), comparably little is known about the in applications highly important multi-dimensional setting, particularly when b is modelled in a nonparametric or high-dimensional way.”