Estimation and inference for varying coefficient partially nonlinear errors-in-variables models

ABSTRACT

In this article, we study the varying coefficient partially nonlinear model with measurement errors in the nonparametric part. A local corrected profile nonlinear least-square estimation procedure is proposed and the asymptotic properties of the resulting estimators are established. Further, a generalized likelihood ratio (GLR) statistic is proposed to test whether the varying coefficients are constant. The asymptotic null distribution of the statistic is obtained and a residual-based bootstrap procedure is employed to compute the p-value of the statistic. Some simulations are conducted to evaluate the performance of the proposed methods. The results show that the estimating and testing procedures work well in finite samples.

KEYWORDS:

• Bootstrap
• Generalized likelihood ratio test
• Local corrected profile nonlinear least squares
• Measurement error
• Varying coefficient partially nonlinear models

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62G05

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11601419, 11501443, 11661067), Education Office Foundation of Shaanxi Province (2016JK1545), and Education Office Foundation of Xi’an University of Technology (2015CX009, 109-451116001).