IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2108.04852.html
   My bibliography  Save this paper

Multiway empirical likelihood

Author

Listed:
  • 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 Dec 2023.
    • Handle: RePEc:arx:papers:2108.04852
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2108.04852
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Harold D Chiang & Yukun Ma & Joel Rodrigue & Yuya Sasaki, 2021. "Dyadic double/debiased machine learning for analyzing determinants of free trade agreements," Papers 2110.04365, arXiv.org, revised Dec 2022.
    5. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
    6. Konrad Menzel, 2021. "Bootstrap With Cluster‐Dependence in Two or More Dimensions," Econometrica, Econometric Society, vol. 89(5), pages 2143-2188, September.
    7. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    8. Zhouping Li & Jinfeng Xu & Wang Zhou, 2016. "On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 49-69, March.
    9. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    10. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    11. Zang, Yangguang & Zhang, Sanguo & Li, Qizhai & Zhang, Qingzhao, 2016. "Jackknife empirical likelihood test for high-dimensional regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 302-316.
    12. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.
    13. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    14. Harold D Chiang & Bruce E Hansen & Yuya Sasaki, 2022. "Standard errors for two-way clustering with serially correlated time effects," Papers 2201.11304, arXiv.org, revised Dec 2023.
    15. Yukitoshi Matsushita & Taisuke Otsu, 2018. "Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect," The Japanese Economic Review, Japanese Economic Association, vol. 69(2), pages 133-155, June.
    16. Yong Cai, 2022. "Linear Regression with Centrality Measures," Papers 2210.10024, arXiv.org.
    17. Yang, Hanfang & Zhao, Yichuan, 2018. "Smoothed jackknife empirical likelihood for the one-sample difference of quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 58-69.
    18. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.
    19. Li, Minqiang & Peng, Liang & Qi, Yongcheng, 2011. "Reduce computation in profile empirical likelihood method," MPRA Paper 33744, University Library of Munich, Germany.
    20. Zhang, Rongmao & Peng, Liang & Qi, Yongcheng, 2012. "Jackknife-blockwise empirical likelihood methods under dependence," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 56-72, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2108.04852. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.