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.
Keywords Residual-based empirical distribution function - Local linear smoother - Bahadur representation
Mathematics Subject Classification (2000) 62M05 - 62M10 - 62G30
The research of A. Schick was supported in part by NSF Grant DMS0405791.