On minimax identification of nonparametric autoregressive models

被引：0

作者：

Bernard Delyon

Anatoli Juditsky

机构：

[1] IRISA,

[2] Campus de Beaulieu,undefined

[3] 35042 Rennes Cedex,undefined

[4] France e-mail: delyon@math.univ-rennes1.fr,undefined

[5] INRIA Rhône-Alpes,undefined

[6] 655 avenue de l'Europe 38330 Montbonnot Saint Martin,undefined

[7] France e-mail: Anatoli.Iouditski@inrialpes.fr,undefined

来源：

Probability Theory and Related Fields | 2000年 / 116卷

关键词：

Mathematics Subject Classification (1991): 62M05, 62G07, 62M20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider the problem of nonparametric identification for a multi-dimensional functional autoregression yt = f(yt−1, …,yt−d) + et on the basis of N observations of yt. In the case when the unknown nonlinear function f belongs to the Barron class, we propose an estimation algorithm which provides approximations of f with expected L2 accuracy O(N1/4ln1/4N). We also show that this approximation rate cannot be significantly improved.

引用

页码：21 / 39

页数：18

共 50 条

[1] On minimax identification of nonparametric autoregressive models
Delyon, B
Juditsky, A
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2000, 116 (01) : 21 - 39
[2] On nonergodicity for nonparametric autoregressive models
Tang, Mingtian
Wang, Yunyan
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,
[3] On nonergodicity for nonparametric autoregressive models
Mingtian Tang
Yunyan Wang
[J]. Advances in Difference Equations, 2013
[4] Nonparametric identification for nonlinear autoregressive time series models: Convergence rates
Lu, ZD
Cheng, P
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 1999, 20 (02) : 173 - 184
[5] Bayesian nonparametric vector autoregressive models
Kalli, Maria
Griffin, Jim E.
[J]. JOURNAL OF ECONOMETRICS, 2018, 203 (02) : 267 - 282
[6] System identification using autoregressive Bayesian neural networks with nonparametric noise models
Merkatas, Christos
Sarkka, Simo
[J]. JOURNAL OF TIME SERIES ANALYSIS, 2023, 44 (03) : 319 - 330
[7] A nonparametric test of conditional autoregressive heteroscedasticity for threshold autoregressive models
Chen, M
Chen, GM
[J]. CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2001, 29 (04): : 649 - 666
[8] Nonparametric likelihood inference for general autoregressive models
Bravo, Francesco
[J]. STATISTICAL METHODS AND APPLICATIONS, 2010, 19 (01): : 79 - 106
[9] Sequential Adaptive Estimators in Nonparametric Autoregressive Models
Arkoun, Ouerdia
[J]. SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS, 2011, 30 (02): : 229 - 247
[10] Nonparametric likelihood inference for general autoregressive models
Francesco Bravo
[J]. Statistical Methods and Applications, 2010, 19 : 79 - 106

← 1 2 3 4 5 →