Nonparametric adaptive estimation for integrated diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Comte, F.¹  Genon-Catalot, V.¹  Rozenholc, Y.¹ 

[1] Univ Paris 05, MAP5, CNRS, UMR 8145, Paris, France

关键词: Adaptive estimation;    Diffusion process;    Drift;    Diffusion coefficient;    Mean square estimator;    Model selections;    Integrated process;    Discrete observation;   

DOI  :  10.1016/j.spa.2008.04.009

来源: Elsevier

【 摘 要 】

Let (V-t) he a stationary and beta-mixing diffusion with unknown drift and diffusion coefficient. The integrated process X-t = integral(t)(0) V(s)ds is observed at discrete times with regular sampling interval Delta. For both the drift function and the diffusion coefficient Of the unobserved diffusion (VI), we build nonparametric adaptive estimators based on a penalized least square approach. We derive risk bounds for the estimators. Interpreting these bounds through the asymptotic framework of high frequency data, we show that Our estimators reach the minimax optimal rates of convergence, under sonic constraints on the sampling interval. The algorithms of estimation are implemented for several examples of diffusion models. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free