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Semiparametric efficient inferences for generalised partially linear models

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  • Jafer Rahman
  • Shihua Luo
  • Yawen Fan
  • Xiaohui Liu

Abstract

In this paper, we consider semiparametric efficient inferences in the generalised partially linear models. A novel bias-corrected estimating procedure and a bias-corrected empirical log-likelihood ratio are developed, respectively, for point estimation and confidence regions for parameters of interest. Under mild conditions, the resulting likelihood ratio is shown to be standard chi-squared distributed asymptotically. Moreover, it is noteworthy that the range of bandwidth in this paper covers the optimal bandwidth due to the implementation of a new bias-corrected technique. Therefore, no undersmoothing is needed here for guaranteeing the asymptotically standard chi-squared distribution of the proposed statistic. Simulation study and real application are also provided in order to illustrate the performance of resulting procedure.

Suggested Citation

  • Jafer Rahman & Shihua Luo & Yawen Fan & Xiaohui Liu, 2020. "Semiparametric efficient inferences for generalised partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 704-724, July.
    • Handle: RePEc:taf:gnstxx:v:32:y:2020:i:3:p:704-724
    DOI: 10.1080/10485252.2020.1790557
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    Cited by:

    1. Ferrando, L. & Epifanio, I. & Ventura-Campos, N., 2021. "Ordinal classification of 3D brain structures by functional data analysis," Statistics & Probability Letters, Elsevier, vol. 179(C).
    2. Lu Wang & Zhongzhe Ouyang & Xihong Lin, 2024. "Doubly Robust Estimation and Semiparametric Efficiency in Generalized Partially Linear Models with Missing Outcomes," Stats, MDPI, vol. 7(3), pages 1-20, August.

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