NONPARAMETRIC FUNCTION ESTIMATION FOR TIME-SERIES BY LOCAL AVERAGE ESTIMATORS

• 成果类型: Article
• 署名作者: TRAN, LT
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349163
• 发表日期: 1993
• 页码: 1040-1057
• 关键词: DENSITY-ESTIMATION; REGRESSION ESTIMATION; mixing properties; CONVERGENCE; dependence; Consistency; prediction; models; rates

摘要

Let (X(t), Y(t)) be a stationary time series with X(t) being R(d)-valued and Y(t) real valued, and where Y(t) is not necessarily bounded. Let E(Y0\X0) be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence (n-1 log n)1/(d+2) in L(infinity) norm restricted to a compact. The result answers a question raised by Truong and Stone.