Abstract
In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.
| Original language | English |
|---|---|
| Journal | Journal of Nonparametric Statistics |
| DOIs | |
| Publication status | Published - 1 Jan 2019 |
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Keywords
- 62G05
- 62G08
- adaptive estimation
- asymptotic efficiency
- Improved non-asymptotic estimation
- James–Stein procedures
- Lévy process
- model selection
- nonparametric regression
- robust quadratic risk
- sharp oracle inequality
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Improved robust model selection methods for a Lévy nonparametric regression in continuous time. / Pchelintsev, E. A.; Pchelintsev, V. A.; Pergamenshchikov, S. M.
In: Journal of Nonparametric Statistics, 01.01.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Improved robust model selection methods for a Lévy nonparametric regression in continuous time
AU - Pchelintsev, E. A.
AU - Pchelintsev, V. A.
AU - Pergamenshchikov, S. M.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.
AB - In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.
KW - 62G05
KW - 62G08
KW - adaptive estimation
KW - asymptotic efficiency
KW - Improved non-asymptotic estimation
KW - James–Stein procedures
KW - Lévy process
KW - model selection
KW - nonparametric regression
KW - robust quadratic risk
KW - sharp oracle inequality
UR - http://www.scopus.com/inward/record.url?scp=85065075839&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065075839&partnerID=8YFLogxK
U2 - 10.1080/10485252.2019.1609672
DO - 10.1080/10485252.2019.1609672
M3 - Article
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
SN - 1048-5252
ER -