Adaptive estimation of mean and volatility functions in (auto-)regressive models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:97

Article

Comte, F ; Rozenholc, Y

关键词: nonparametric regression;    least-squares estimator;    adaptive estimation;    autoregression;    variance estimation;    mixing processes;   

DOI  :  10.1016/S0304-4149(01)00128-4

来源: Elsevier

【 摘 要 】

In this paper, we study the problem of nonparametric estimation of the mean and variance functions b and sigma (2) in a model: Xi+1 = b(X-i)+sigma (X-i)epsilon (i+1). For this purpose, we consider a collection of finite dimensional linear spaces. We ]estimate b using a mean squares estimator built on a data driven selected linear space among the collection. Then an analogous procedure estimates sigma (2), using a possibly different collection of models. Both data driven choices are performed via the minimization of penalized mean squares contrasts. The penalty functions are random in order not to depend on unknown variance-type quantities. In all cases, we state nonasymptotic risk bounds in L-2 empirical norm for our estimators and we show that they are both adaptive in the minimax sense over a large class of Besov balls. Lastly, we give the results of intensive simulation experiments which show the good performances of our estimator. (C) 2002 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free