Geodesic
Improved nonparametric estimation of the drift in diffusion processes
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 364-372

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In this paper, we have considered the robust adaptive nonparametric estimation problem for the drift coefficient in diffusion processes. It has been shown that the initial estimation problem can be reduced to the estimation problem in a discrete time nonparametric heteroscedastic regression model by using the sequential approach. We have developed a new sharp model selection method for estimating the unknown drift function using the improved estimation approach. An adaptive model selection procedure based on the improved weighted least square estimates has been proposed. It has been established that such estimate outperforms in non-asymptotic mean square accuracy the procedure based on the classical weighted least square estimates. Sharp oracle inequalities for the robust risk have been obtained.
Keywords: improved estimation, mean-square accuracy, model selection, sharp oracle inequality.
Mots-clés : stochastic diffusion process 
@article{UZKU_2018_160_2_a17,
     author = {E. A. Pchelintsev and S. S. Perelevskiy and I. A. Makarova},
     title = {Improved nonparametric estimation of the drift in diffusion processes},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {364--372},
     publisher = {mathdoc},
     volume = {160},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a17/}
}
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E. A. Pchelintsev; S. S. Perelevskiy; I. A. Makarova. Improved nonparametric estimation of the drift in diffusion processes. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 364-372. http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a17/