Annals of Statistics

Spline-backfitted kernel smoothing of nonlinear additive autoregression model

Li Wang and Lijian Yang

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Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the “curse of dimensionality.” Under rather weak conditions, we propose spline-backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high-dimensional time series, and theoretically reliable so inference can be made on the component functions with confidence. Simulation experiments have provided strong evidence that corroborates the asymptotic theory.

Article information

Ann. Statist., Volume 35, Number 6 (2007), 2474-2503.

First available in Project Euclid: 22 January 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G08: Nonparametric regression

Bandwidths B spline knots local linear estimator mixing Nadaraya–Watson estimator nonparametric regression


Wang, Li; Yang, Lijian. Spline-backfitted kernel smoothing of nonlinear additive autoregression model. Ann. Statist. 35 (2007), no. 6, 2474--2503. doi:10.1214/009053607000000488.

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