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Multiway empirical likelihood

Author

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  • Harold D Chiang
  • Yukitoshi Matsushita
  • Taisuke Otsu

Abstract

This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under the non-degenerate case, where corresponding Hoeffding type decomposition is dominated by linear terms. Our methodology is related to the notion of jackknife empirical likelihood but the leave-out pseudo values are constructed by leaving columns or rows. We further develop a modified version of our multiway empirical likelihood statistic, which converges to a chi-square distribution regardless of the degeneracy, and discover its desirable higher-order property compared to the t-ratio by the conventional Eicker-White type variance estimator. The proposed methodology is illustrated by several important statistical problems, such as bipartite network, generalized estimating equations, and three-way observations.

Suggested Citation

  • Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2108.04852
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    3. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    4. Bryan S. Graham & Fengshi Niu & James L. Powell, 2019. "Kernel Density Estimation for Undirected Dyadic Data," Papers 1907.13630, arXiv.org.
    5. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    6. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    7. 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).
    8. Yuan Zhang & Elizaveta Levina & Ji Zhu, 2017. "Estimating network edge probabilities by neighbourhood smoothing," Biometrika, Biometrika Trust, vol. 104(4), pages 771-783.
    9. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2019. "Empirical Process Results for Exchangeable Arrays," Papers 1906.11293, arXiv.org, revised May 2020.
    10. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    11. Puying Zhao & Malay Ghosh & J. N. K. Rao & Changbao Wu, 2020. "Bayesian empirical likelihood inference with complex survey data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(1), pages 155-174, February.
    12. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    13. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2023. "Inference for High-Dimensional Exchangeable Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1595-1605, July.
    14. Y. G. Berger & O. De La Riva Torres, 2016. "Empirical likelihood confidence intervals for complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 319-341, March.
    15. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    16. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
    17. Zhong, Ping-Shou & Chen, Sixia, 2014. "Jackknife empirical likelihood inference with regression imputation and survey data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 193-205.
    18. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.
    19. Bryan S. Graham, 2020. "Sparse Network Asymptotics for Logistic Regression under Possible Misspecification," NBER Working Papers 27962, National Bureau of Economic Research, Inc.
    20. Steffen Lauritzen & Alessandro Rinaldo & Kayvan Sadeghi, 2018. "Random networks, graphical models and exchangeability," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 481-508, June.
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