Efficient prediction for linear and nonlinear autoregressive models

• 成果类型: Article
• 署名作者: Mueller, Ursula U.; Schick, Anton; Wefelmeyer, Wolfgang
• 署名单位: Texas A&M University System; Texas A&M University College Station; State University of New York (SUNY) System; Binghamton University, SUNY; University of Cologne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000812
• 发表日期: 2006
• 页码: 2496-2533
• 关键词: smoothed empirical processes; Nonparametric Function Estimation; transition distribution function; moving average processes; time-series; density estimators; WEAK-CONVERGENCE; Asymptotic Normality; Markov Process; censored-data

摘要

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.