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Two-Step Semiparametric Empirical Likelihood Inference

Author

Listed:
  • Bravo, Francesco
  • Juan Carlos, Escanciano
  • Ingrid Van Keilegom, Ingrid

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.

Suggested Citation

  • Bravo, Francesco & Juan Carlos, Escanciano & Ingrid Van Keilegom, Ingrid, 2020. "Two-Step Semiparametric Empirical Likelihood Inference," LIDAM Reprints ISBA 2020046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020046
    DOI: https://doi.org/10.1214/18-AOS1788
    Note: In: Annals of Statistics, Vol. 48, no. 1, p. 1-26 (2020)
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    Citations

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    Cited by:

    1. Matsushita, Yukitoshi & Otsu, Taisuke, 2020. "Likelihood inference on semiparametric models with generated regressors," LSE Research Online Documents on Economics 102696, London School of Economics and Political Science, LSE Library.
    2. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    3. Adusumilli, Karun & Otsu, Taisuke & Qiu, Chen, 2023. "Reweighted nonparametric likelihood inference for linear functionals," LSE Research Online Documents on Economics 120198, London School of Economics and Political Science, LSE Library.
    4. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    5. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Aug 2024.
    6. Tang, Shengfang & Huang, Zhilin, 2022. "Empirical likelihood confidence interval for difference-in-differences estimator with panel data," Economics Letters, Elsevier, vol. 216(C).
    7. Harold D. Chiang & Bing Yang Tan, 2020. "Empirical likelihood and uniform convergence rates for dyadic kernel density estimation," Papers 2010.08838, arXiv.org, revised May 2022.
    8. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Xue, Liugen, 2024. "Empirical likelihood in a partially linear single-index model with censored response data," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).
    10. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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