Identification for partially linear regression model with autoregressive errors

Abstract

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.

Keywords:

• Autoregressive errors
• partially linear model
• structure identification

Acknowledgments

We would like to sincerely thank the AE and anonymous reviewer for their constructive and substantial comments which led us to put more details in the paper and significantly improved the presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The third author's research was supported in part by the National Research Foundation (NRF) of South Africa SARChI Research Chair UID: 71199 and Re:IFR170227223754 grant no. 109214.