Local linear spatial regression

• 成果类型: Article
• 署名作者: Hallin, M; Lu, ZD; Tran, LT
• 署名单位: Universite Libre de Bruxelles; Chinese Academy of Sciences; University of London; London School Economics & Political Science; Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000850
• 发表日期: 2004
• 页码: 2469-2500
• 关键词: kernel density-estimation; nonlinear time-series; central limit-theorem; random-fields; nonparametric-estimation; Asymptotic Normality; stationary-processes; variable bandwidth; strong consistency; mixing sequences

摘要

A local linear kernel estimator of the regression function x --> g(x) := E[Y-i\X-i = x], X is an element of R-d, of a stationary (d + 1)-dimensional spatial process {(Y-i, X-i), i is an element of Z(N)} observed over a rectangular domain of the form l(n) := {i = (i(1),..., i(N)) is an element of Z(N)\ 1 less than or equal to i(k) less than or equal to n(k), k = 1,..., N}, n = (n(1),..., n(N)) is an element of Z(N), is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is assumed to satisfy some very general mixing conditions, generalizing classical time-series strong mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different rates depending on the direction in Z(N).