NONPARAMETRIC FUNCTION ESTIMATION INVOLVING TIME-SERIES

• 成果类型: Article
• 署名作者: TRUONG, YK; STONE, CJ
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348513
• 发表日期: 1992
• 页码: 77-97
• 关键词: dependent observations; REGRESSION ESTIMATION; uniform consistency; kernel estimators; CONVERGENCE; prediction; rates

摘要

Consider a stationary time series (X(t), Y(t)), t = 0, +/- 1,..., with X(t) being R(d)-valued and Y(t) real-valued. The conditional mean function is given by theta(X0) = E(Y0\X0). Under appropriate regularity conditions, a local average estimator of this function based on a finite realization (X1, Y1),..., (X(n), Y(n)) can be chosen to achieve the optimal rate of convergence n-1/(2+d) both pointwise and in L2 norms restricted to a compact; and it can also be chosen to achieve the optimal rate of convergence (n-1 log(n))1/(2+d) in L infinity norm restricted to a compact. Similar results hold for local median estimators of the conditional median function, which is given by theta(X0) = med(Y0\X0).