Uniformly root-N consistent density estimators for weakly dependent invertible linear processes

• 成果类型: Article
• 署名作者: Schick, Anton; Wefelmeyer, Wolfgang
• 署名单位: 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: 10.1214/009053606000001352
• 发表日期: 2007
• 页码: 815-843
• 关键词: moving average processes; central-limit-theorem; Asymptotic Normality; Functional Estimation; stationary-processes; convergence-rates; marginal density; mixing processes; kernel estimate; time-series

摘要

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n(-1/2). Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.