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High-dimensional empirical likelihood inference

Author

Listed:
  • Jinyuan Chang
  • Song Xi Chen
  • Cheng Yong Tang
  • Tong Tong Wu

Abstract

SummaryHigh-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. Second, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. Numerical studies demonstrate promising performance and potential practical benefits of the new methods.

Suggested Citation

  • Jinyuan Chang & Song Xi Chen & Cheng Yong Tang & Tong Tong Wu, 2021. "High-dimensional empirical likelihood inference," Biometrika, Biometrika Trust, vol. 108(1), pages 127-147.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:1:p:127-147.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa051
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    Citations

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    Cited by:

    1. Victor Chernozhukov & Iv'an Fern'andez-Val & Chen Huang & Weining Wang, 2024. "Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models," Papers 2402.00584, arXiv.org.
    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. Chang, Jinyuan & Jiang, Qing & Shao, Xiaofeng, 2023. "Testing the martingale difference hypothesis in high dimension," Journal of Econometrics, Elsevier, vol. 235(2), pages 972-1000.

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