TY  - JOUR
AU  - You, Jinhong 
AU  - Chen, Gemai 
AU  - Zhou, Xian 
PY  - 2005
TI  - β-Spline Estimation in a Semiparametric Regression Model with Nonlinear Time Series Errors
JF  - American Journal of Applied Sciences
VL  - 2
IS  - 9
DO  - 10.3844/ajassp.2005.1343.1349
UR  - https://thescipub.com/abstract/ajassp.2005.1343.1349
AB  - 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 B-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 B-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.