The Annals of Statistics

Time-varying nonlinear regression models: Nonparametric estimation and model selection

Ting Zhang and Wei Biao Wu

Full-text: Open access

Abstract

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results are applied to the U.S. Treasury interest rate data.

Article information

Source
Ann. Statist., Volume 43, Number 2 (2015), 741-768.

Dates
First available in Project Euclid: 3 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1425398507

Digital Object Identifier
doi:10.1214/14-AOS1299

Mathematical Reviews number (MathSciNet)
MR3319142

Zentralblatt MATH identifier
1312.62046

Subjects
Primary: 62G05: Estimation 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Information criterion local linear estimation nonparametric model selection nonstationary processes time-varying nonlinear regression models

Citation

Zhang, Ting; Wu, Wei Biao. Time-varying nonlinear regression models: Nonparametric estimation and model selection. Ann. Statist. 43 (2015), no. 2, 741--768. doi:10.1214/14-AOS1299. https://projecteuclid.org/euclid.aos/1425398507


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