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Empirical-Likelihood-Based Inference for Partially Linear Models

Author

Listed:
  • Haiyan Su

    (School of Computing, Montclair State University, Montclair, NJ 07043, USA)

  • Linlin Chen

    (Department of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY 14632, USA)

Abstract

Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical inference for the parametric component effects within these models, employing a nonparametric empirical likelihood approach. The proposed method involves a projection step to eliminate the nuisance nonparametric component and utilizes an empirical-likelihood-based technique, along with the Bartlett correction, to enhance the coverage probability of the confidence interval for the parameter of interest. This method demonstrates robustness in handling normally and non-normally distributed errors. The proposed empirical likelihood ratio statistic converges to a limiting chi-square distribution under certain regulations. Simulation studies demonstrate that this method provides better inference in terms of coverage probabilities compared to the conventional normal-approximation-based method. The proposed method is illustrated by analyzing the Boston housing data from a real study.

Suggested Citation

  • Haiyan Su & Linlin Chen, 2024. "Empirical-Likelihood-Based Inference for Partially Linear Models," Mathematics, MDPI, vol. 12(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:162-:d:1313117
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    References listed on IDEAS

    as
    1. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.
    2. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    3. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    4. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    Full references (including those not matched with items on IDEAS)

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