The semiparametric partial linear models are often used in real data analysis for its flexibility and parsimony. Statistical inference of this model is restricted with two conditions: (i) the linear and nonlinear parts are known in advance, (ii) the errors are independent. However, in practice, this is unreasonable to artificially determine which subset of variables have linear effect on the response and which have nonlinear effect. In addition, the assumption of errors being independent may be incorrect for time series data. Therefore, it is of great interest to develop some efficient methods to distinguish linear components from nonlinear ones with correlated errors. In this paper, we develop a method for identifying linear and nonlinear components, and estimate the coefficients of error structure. The performance of the proposed method is examined by simulation study and analyses a real data set for an illustration.

半参数部分线性模型因其灵活性和简约性而经常在实际数据分析中使用。该模型的统计推断受到两个条件的限制：（i）线性和非线性部分是事先已知的，（ii）误差是独立的。但是，在实践中，人为地确定哪些变量子集对响应具有线性影响而哪些变量具有非线性影响是不合理的。另外，对于时间序列数据，错误独立的假设可能是不正确的。因此，开发一些有效的方法来将线性分量与具有相关误差的非线性分量区分开来是非常有意义的。在本文中，我们开发了一种识别线性和非线性分量的方法，并估计误差结构的系数。