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Estimation and variable selection for generalised partially linear single-index models

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  • Peng Lai
  • Ye Tian
  • Heng Lian

Abstract

In this paper, we study the problem of estimation and variable selection for generalised partially linear single-index models based on quasi-likelihood, extending existing studies on variable selection for partially linear single-index models to binary and count responses. To take into account the unit norm constraint of the index parameter, we use the 'delete-one-component' approach. The asymptotic normality of the estimates is demonstrated. Furthermore, the smoothly clipped absolute deviation penalty is added for variable selection of parameters both in the nonparametric part and the parametric part, and the oracle property of the variable selection procedure is shown. Finally, some simulation studies are carried out to illustrate the finite sample performance.

Suggested Citation

  • Peng Lai & Ye Tian & Heng Lian, 2014. "Estimation and variable selection for generalised partially linear single-index models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 171-185, March.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:171-185
    DOI: 10.1080/10485252.2013.841156
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    Cited by:

    1. Mohamed Alahiane & Idir Ouassou & Mustapha Rachdi & Philippe Vieu, 2022. "High-Dimensional Statistics: Non-Parametric Generalized Functional Partially Linear Single-Index Model," Mathematics, MDPI, vol. 10(15), pages 1-21, July.
    2. Mustapha Rachdi & Mohamed Alahiane & Idir Ouassou & Abdelaziz Alahiane & Lahoucine Hobbad, 2024. "Cross-Validated Functional Generalized Partially Linear Single-Functional Index Model," Mathematics, MDPI, vol. 12(17), pages 1-22, August.
    3. Mohamed Alahiane & Idir Ouassou & Mustapha Rachdi & Philippe Vieu, 2021. "Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)," Stats, MDPI, vol. 4(4), pages 1-21, September.

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