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Effects of data dimension on empirical likelihood

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  • Song Xi Chen
  • Liang Peng
  • Ying-Li Qin

Abstract

We evaluate the effects of data dimension on the asymptotic normality of the empirical likelihood ratio for high-dimensional data under a general multivariate model. Data dimension and dependence among components of the multivariate random vector affect the empirical likelihood directly through the trace and the eigenvalues of the covariance matrix. The growth rates to infinity we obtain for the data dimension improve the rates of Hjort et al. (2008). Copyright 2009, Oxford University Press.

Suggested Citation

  • Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:711-722
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    Cited by:

    1. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    2. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    3. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    4. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    5. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    6. Liu, Zhi & Xia, Xiaochao & Zhou, Wang, 2015. "A test for equality of two distributions via jackknife empirical likelihood and characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 97-114.
    7. Yukun Liu & Changliang Zou & Zhaojun Wang, 2013. "Calibration of the empirical likelihood for high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 529-550, June.
    8. Li, Gao-Rong & Zhu, Li-Ping & Zhu, Li-Xing, 2010. "Adaptive confidence region for the direction in semiparametric regressions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1364-1377, July.
    9. Francesco Giordano & Soumendra Nath Lahiri & Maria Lucia Parrella, 2014. "GRID for model structure discovering in high dimensional regression," Working Papers 3_231, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    10. Du, Xiaojie & Schick, Anton, 2018. "Signed rank based empirical likelihood for the symmetric location model," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 40-45.
    11. Ursula U. Müller & Hanxiang Peng & Anton Schick, 2019. "Inference about the slope in linear regression: an empirical likelihood approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 181-211, February.
    12. Tang, Xingyu & Li, Jianbo & Lian, Heng, 2013. "Empirical likelihood for partially linear proportional hazards models with growing dimensions," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 22-32.
    13. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    14. Bin Guo & Song Xi Chen, 2016. "Tests for high dimensional generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1079-1102, November.
    15. Changliang Zou & Liuhua Peng & Long Feng & Zhaojun Wang, 2014. "Multivariate sign-based high-dimensional tests for sphericity," Biometrika, Biometrika Trust, vol. 101(1), pages 229-236.
    16. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    17. Mahdieh Bayati & Seyed Kamran Ghoreishi & Jingjing Wu, 2021. "Bayesian analysis of restricted penalized empirical likelihood," Computational Statistics, Springer, vol. 36(2), pages 1321-1339, June.
    18. Ying Sheng & Yifei Sun & Chiung‐Yu Huang & Mi‐Ok Kim, 2022. "Synthesizing external aggregated information in the presence of population heterogeneity: A penalized empirical likelihood approach," Biometrics, The International Biometric Society, vol. 78(2), pages 679-690, June.
    19. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    20. 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.
    21. Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
    22. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    23. Peng, Hanxiang & Schick, Anton, 2018. "Asymptotic normality of quadratic forms with random vectors of increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 22-39.
    24. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    25. repec:cep:stiecm:/2014/574 is not listed on IDEAS

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