Abstract
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.
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The research of A. Schick was supported in part by NSF Grant DMS0405791.
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Müller, U.U., Schick, A. & Wefelmeyer, W. Estimating the innovation distribution in nonparametric autoregression. Probab. Theory Relat. Fields 144, 53–77 (2009). https://doi.org/10.1007/s00440-008-0141-2
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DOI: https://doi.org/10.1007/s00440-008-0141-2