Estimation and hypothesis test for varying coefficient single-index multiplicative models

ABSTRACT

Estimation and hypothesis test for varying coefficient single-index multiplicative models are considered in this paper. To estimate an unknown single-index parameter, a profile product relative error estimation is proposed for the single-index parameter with a leave-one-component-out estimation method. A Wald-type test statistic is proposed to test a linear hypothesis test of the single-index. We employ the smoothly clipped absolute deviation penalty to simultaneously select variables and estimate regression coefficients. To study the model checking problem, we propose a variant of the integrated conditional moment test statistic by using a linear projection weighting function, and we also suggest a bootstrap procedure for calculating critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

KEYWORDS:

• Local linear smoothing
• model checking
• profile least product relative error estimator
• single-index
• variable selection

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 62E20
• 62F03
• 62F05

Acknowledgments

The authors thank the editor, the associate editor, and two referees for their constructive suggestions that helped us to improve the early manuscript.

Disclosure statement

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

Additional information

Funding

Jun Zhang’s research was supported by the National Natural Science Foundation of China [grant number 12371448]. Xuehu Zhu’s research described herewith was supported by a grant from the National Social Science Foundation of China [grant number 21BTJ048], and two grants from the National Natural Science Foundation of China [grant numbers 12371276 and 12131006]. Gaorong Li’s research was supported by the National Natural Science Foundation of China [grant numbers 12271046 and12131006].