Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled-data

作     者：Bosq, D Cheze-Payaud, N 

作者机构：Univ Paris 06 F-75252 Paris 05 France Univ Paris 10 F-92000 Nanterre France 

出 版 物：《STATISTICS》 (统计学)

年 卷 期：1999年第32卷第3期

页      面：229-247页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

主　　题：nonparametric regression estimation sampled data mixing continuous-parameter processes quadratic-mean convergence choice of bandwidth 

摘      要：For different classes of deterministic and random sampling (t(k)), we establish the asymptotic expressions for the bias and the variance of the estimate r(n)(x) based on sampled data (X-tk, Y-tk)k=1,...,n for the regression function r(x) = E(Y-t/X-t = x) of unbounded continuous-time processes (X-t, Y-t)(t is an element of R) (not necessarily stationary). Under mild mixing conditions, we show that r(n)(x) has exactly the same asymptotic quadratic error as in the i.i.d. case. In order to prove this result, we use some large deviations inequalities for mixing processes.