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Use generalized linear models or generalized partially linear models?

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Abstract

We propose test statistics based on the penalized spline to decide between generalized linear models and generalized partially linear models. The numerical performance of the proposed statistics is comparable to that of their kernel-based competitors, which have been shown to be asymptotically normal in the literature (Härdle et al. in J Am Stat Assoc 93:1461–1474, 1998). We also numerically explore the possibility of using the proposed statistics for goodness of fit checking for GLM. The proposed proposed procedures are illustrated to analyze two datasets.

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Acknowledgements

Li’s research was partially supported by NNSFC grant 11871294. Härdle gratefully acknowledges the financial support of the European Union’s Horizon 2020 research and innovation program “FIN-TECH: A Financial supervision and Technology compliance training programme" under the grant agreement No 825215 (Topic: ICT-35-2018, Type of action: CSA), the European Cooperation in Science & Technology COST Action grant CA19130—Fintech and Artificial Intelligence in Finance—Towards a transparent financial industry, the Deutsche Forschungsgemeinschaft’s IRTG 1792 grant.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, Shandong, China

    Xinmin Li

  2. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Haozhe Liang

  3. Institut für Statistik und Ökonometrie, Humboldt-Universität zu Berlin, 10178, Berlin, Germany

    Wolfgang Härdle

  4. Department of Statistics, George Washington University, Washington, DC, USA

    Hua Liang

Authors
  1. Xinmin Li
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  2. Haozhe Liang
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  3. Wolfgang Härdle
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  4. Hua Liang
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Contributions

LXM and LH wrote the main manuscript text, LHZ helped the program, HW commented on the methodological section. All authors reviewed the manuscript

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Correspondence to Hua Liang.

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Li, X., Liang, H., Härdle, W. et al. Use generalized linear models or generalized partially linear models?. Stat Comput 33, 101 (2023). https://doi.org/10.1007/s11222-023-10278-4

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  • DOI: https://doi.org/10.1007/s11222-023-10278-4

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