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

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  • Mengyao Li
  • Jiangshe Zhang
  • Jun Zhang

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.

Suggested Citation

  • Mengyao Li & Jiangshe Zhang & Jun Zhang, 2025. "Projection tests for regression coefficients in high-dimensional partial linear models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(10), pages 3024-3051, May.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:10:p:3024-3051
    DOI: 10.1080/03610926.2024.2383646
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