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Title: β-spline estimation in a semiparametric regression model with nonlinear time series errors
Authors: You, JH
Chen, G
Zhou, X
Keywords: Semiparametric regression model
first-order Markovian bilinear process
β-splines series estimation
semiparametric least squares estimators
asymptotic normality
Issue Date: 2005
Publisher: Science Publications
Source: American journal of applied sciences, 2005, v. 2, no. 9, p. 1343-1349 How to cite?
Journal: American journal of applied sciences 
Abstract: We study the estimation problems for a partly linear regression model with a nonlinear time series error structure. The model consists of a parametric linear component for the regression coefficients and a nonparametric nonlinear component. The random errors are unobservable and modeled by a first-order Markov bilinear process. Based on a β-spline series approximation of the nonlinear component function, we propose a semiparametric ordinary least squares estimator and a semiparametric generalized least squares estimator of the regression coefficients, a least squares estimator of the autoregression parameter for the errors, and a β-spline series estimator of the nonparametric component function. The asymptotic properties of these estimators are investigated and their asymptotic distributions are derived. We also provide a consistent estimator for the asymptotic covariance matrix of the semiparametric generalized least squares estimator of the regression coefficients. Our results can be used to make asymptotically efficient statistical inferences. In addition, a small simulation is conducted to evaluate the performance of the proposed estimators, which shows that the semiparametric generalized least squares estimator of the regression coefficients is more efficient than the semiparametric ordinary least squares estimator.
ISSN: 1546-9239 (print)
1554-3641 (online)
DOI: 10.3844/ajassp.2005.1343.1349
Rights: © 2005 Jinhong You, Gemai Chen and Xian Zhou.
This is an open access article distributed under the terms of the Creative Commons Attribution License ( , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The following publication You, J., Chen, G., & Zhou, X. (2005). B-Spline Estimation in a Semiparametric Regression Model with Nonlinear Time Series Errors. American Journal o/Applied Sciences, 2(9), 1343-1349 is available at
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