Estimating the innovation distribution in nonparametric autoregression

• 成果类型: Article
• 署名作者: Mueller, Ursula U.; Schick, Anton; Wefelmeyer, Wolfgang
• 署名单位: State University of New York (SUNY) System; Binghamton University, SUNY; Texas A&M University System; Texas A&M University College Station; University of Cologne
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0141-2
• 发表日期: 2009
• 页码: 53-77
• 关键词: empirical distribution function; WEAK-CONVERGENCE; asymptotic-behavior; error distribution; squared residuals; GARCH MODELS; regression; ergodicity; ARCH; parameters

摘要

We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregressive model. The residuals are based on a local linear smoother for the autoregression function. Our result implies a functional central limit theorem for the residual-based estimator.