Projection tests for regression coefficients in high-dimensional partial linear models

Abstract.

To check the significance of the regression coefficients in the linear component of high-dimensional partial linear models, we proposed some projection-based test statistics. These test statistics are connected with U-statistics of order two and they are applicable for diverging dimensions and heteroscedastic model errors. By using the martingale central limit theorem, we show the asymptotic normalities of the proposed test statistics under the null hypothesis and local alternative hypotheses. The performance of test statistics are evaluated by simulation studies. The simulation results show that the proposed test statistics are powerful and have the correct type-I error asymptotically under the null hypothesis.

Keywords:

• Kernel smoothing
• partial linear models
• projection tests

Mathematics Subject Classification 2020::

• 62G05
• 62G08
• 62G20

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 authors.

Additional information

Funding

Mengyao Li’s research was supported by the National Social Science Foundation of China (Grant No. 21BTJ048, Principal Investigator, 2021.06-2024.06). Jiangshe Zhang’s research was supported by the National Natural Science Foundation of China (Grant No. 12371512). Jun Zhang’s research was supported by the National Natural Science Foundation of China (Grant No. 12371448).