On minimax identification of nonparametric autoregressive models

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• 作者：Bernard Delyon and Anatoli Juditsky
• 关键词：Mathematics Subject Classification (1991) ; 62M05 ; 62G07 ; 62M20
• 刊名：Probability Theory and Related Fields
• 出版年：2000
• 出版时间：January 2000
• 年：2000
• 卷：116
• 期：1
• 页码：21-39
• 全文大小：125 KB

文摘

We consider the problem of nonparametric identification for a multi-dimensional functional autoregression y _t = f(y _{t −1}, …,y _t−d ) + e _t on the basis of N observations of y _t . 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 L ₂ accuracy O(N 1/4ln1/4 N). We also show that this approximation rate cannot be significantly improved. The proposed algorithms are “computationally efficient”– the total number of elementary computations necessary to complete the estimate grows polynomially with N.