Estimating the innovation distribution in nonparametric autoregression

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...

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Veröffentlicht in:	Probability theory and related fields 2009-05, Vol.144 (1-2), p.53-77
Hauptverfasser:	Müller, Ursula U., Schick, Anton, Wefelmeyer, Wolfgang
Format:	Artikel
Sprache:	eng
Schlagworte:	Autoregressive models Bandwidths Central limit theorem Distribution functions Distribution theory Economics Estimating techniques Exact sciences and technology Finance General topics Guarantees Innovations Insurance Limit theorems Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonparametric statistics Operations Research/Decision Theory Probability Probability and statistics Probability Theory and Stochastic Processes Quantitative Finance Regression analysis Sciences and techniques of general use Statistics for Business Stochastic models Studies Theoretical Theoretical mathematics Time series
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Beschreibung
Zusammenfassung:	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.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-008-0141-2