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A robust adaptive-to-model enhancement test for parametric single-index models

Author

Listed:
  • Cuizhen Niu

    (Beijing Normal University)

  • Lixing Zhu

    (Beijing Normal University
    Hong Kong Baptist University)

Abstract

This paper is devoted to test the parametric single-index structure of the underlying model when there are outliers in observations. First, a test that is robust against outliers is suggested. The Hampel’s second-order influence function of the test statistic is proved to be bounded. Second, the test fully uses the dimension reduction structure of the hypothetical model and automatically adapts to alternative models when the null hypothesis is false. Thus, the test can greatly overcome the dimensionality problem and is still omnibus against general alternative models. The performance of the test is demonstrated by both Monte Carlo simulation studies and an application to a real dataset.

Suggested Citation

  • Cuizhen Niu & Lixing Zhu, 2018. "A robust adaptive-to-model enhancement test for parametric single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1013-1045, October.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:5:d:10.1007_s10463-017-0626-9
    DOI: 10.1007/s10463-017-0626-9
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    References listed on IDEAS

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    Cited by:

    1. Chen, Feifei & Jiang, Qing & Feng, Zhenghui & Zhu, Lixing, 2020. "Model checks for functional linear regression models based on projected empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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