1932

Abstract

Empirical likelihood is a popular nonparametric analog of the usual parametric likelihood, inheriting many of the large-sample properties of the latter construct. This article presents a review of the empirical likelihood approach from its introduction 30 years ago, up to recent theoretical developments. Aspects of computation and connections between empirical likelihood and other likelihood-type quantities are also explored. The article ends with a discussion of some directions for future research.

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2021-03-07
2024-04-19
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Literature Cited

  1. Adimari G. 1997. Empirical likelihood type confidence intervals under random censorship. Ann. Inst. Stat. Math. 49:447–66
    [Google Scholar]
  2. Baggerly KA. 1998. Empirical likelihood as a goodness-of-fit measure. Biometrika 85:535–47
    [Google Scholar]
  3. Bedoui A, Lazar NA. 2020. Bayesian empirical likelihood for ridge and lasso regressions. Comput. Stat. Data Anal. 145:106917
    [Google Scholar]
  4. Berger YG, De La Riva Torres O 2016. Empirical likelihood confidence intervals for complex sampling designs. J. R. Stat. Soc. Ser. B 78:319–41
    [Google Scholar]
  5. Besag J. 1975. Statistical analysis of non-lattice data. Statistician 24:179–95
    [Google Scholar]
  6. Chan NH, Ling S. 2006. Empirical likelihood for GARCH models. Econom. Theory 22:403–28
    [Google Scholar]
  7. Chen J, Lazar NA. 2010. Quantile estimation for discrete data via empirical likelihood. J. Nonparametric Stat. 22:237–55
    [Google Scholar]
  8. Chen J, Lazar NA. 2012. Selection of working correlation structure in generalized estimating equations. J. Comput. Graph. Stat. 21:18–41
    [Google Scholar]
  9. Chen J, Peng L, Zhao Y 2009. Empirical likelihood based confidence intervals for copulas. J. Multivar. Anal. 100:137–51
    [Google Scholar]
  10. Chen J, Sitter RR. 1999. A pseudo empirical likelihood approach to the effective use of auxiliary information in complex surveys. Stat. Sin. 9:385–406
    [Google Scholar]
  11. Chen J, Sitter RR, Wu C 2002. Using empirical likelihood methods to obtain range restricted weights in regression estimator for surveys. Biometrika 89:230–37
    [Google Scholar]
  12. Chen S, Kim JK. 2014. Population empirical likelihood for nonparametric inference in survey sampling. Stat. Sin. 24:335–55
    [Google Scholar]
  13. Chen SX, Cui H. 2003. An extended empirical likelihood for generalized linear models. Stat. Sin. 13:69–81
    [Google Scholar]
  14. Chen SX, Peng L, Qin YL 2009. Effects of data dimension on empirical likelihood. Biometrika 96:711–22
    [Google Scholar]
  15. Chen SX, Van Keilegom I 2009. A review on empirical likelihood methods for regression. TEST 18:415–47
    [Google Scholar]
  16. Chen X, Xie M. 2014. A split-and-conquer approach for analysis of extraordinarily large data. Stat. Sin. 24:1655–84
    [Google Scholar]
  17. Chib S, Greenberg E. 1995. Understanding the Metropolis-Hastings algorithm. Am. Stat. 49:327–35
    [Google Scholar]
  18. Chuang CS, Chan NH. 2002. Empirical likelihood for autoregressive models, with applications to unstable time series. Stat. Sin. 12:387–407
    [Google Scholar]
  19. Corcoran SA. 1998. Bartlett adjustment of empirical discrepancy statistics. Biometrika 85:967–72
    [Google Scholar]
  20. Cox DR. 1972. Regression models and life-tables. J. R. Stat. Soc. Ser. B 34:187–220
    [Google Scholar]
  21. Cressie N, Read TRC. 1984. Multinomial goodness-of-fit tests. J. R. Stat. Soc. Ser. B 46:440–64
    [Google Scholar]
  22. Deville JC, Sarndal CE. 1992. Calibration estimators in survey sampling. J. Am. Stat. Assoc. 87:376–82
    [Google Scholar]
  23. DiCiccio T, Hall P, Romano J 1991. Empirical likelihood is Bartlett-correctable. Ann. Stat. 19:1053–61
    [Google Scholar]
  24. DiCiccio TJ, Romano JP. 1989. On adjustments based on the signed root of the empirical likelihood ratio statistic. Biometrika 76:447–56
    [Google Scholar]
  25. Efron B. 1979. Bootstrap methods: another look at the jackknife. Ann. Stat. 7:1–26
    [Google Scholar]
  26. Efron B. 1981. Nonparametric standard errors and confidence intervals. Can. J. Stat. 9:139–72
    [Google Scholar]
  27. Ferguson TS. 1974. Prior distributions on spaces of probability measures. Ann. Stat. 2:615–29
    [Google Scholar]
  28. Fisher RA. 1922. On the mathematical foundations of theoretical statistics. Philos. Trans. R. Soc. Lond. Ser. A 222:309–68
    [Google Scholar]
  29. Grendar M, Judge G. 2009a. Asymptotic equivalence of empirical likelihood and Bayesian MAP. Ann. Stat. 37:2445–57
    [Google Scholar]
  30. Grendar M, Judge G. 2009b. Empty set problem of maximum empirical likelihood methods. Electron. J. Stat. 3:1542–55
    [Google Scholar]
  31. Grendar M, Judge GG. 2010. Revised empirical likelihood CUDARE Work. Pap. 91799 Dep. Agric. Res. Econ., Univ. Calif Berkeley:
  32. Hartley HO, Rao JNK. 1968. A new estimation theory for sample surveys. Biometrika 55:547–57
    [Google Scholar]
  33. Hjort NL, McKeague IW, Van Keilegom I 2009. Extending the scope of empirical likelihood. Ann. Stat. 37:1079–111
    [Google Scholar]
  34. Hjort NL, McKeague IW, Van Keilegom I 2018. Hybrid combinations of parametric and empirical likelihoods. Stat. Sin. 28:2389–407
    [Google Scholar]
  35. Imbens GW, Spady RH, Johnson P 1998. Information theoretic approaches to inference in moment condition models. Econometrica 66:333–57
    [Google Scholar]
  36. Jaeger AP. 2015. Composite empirical likelihood: a derivation of multiple non-parametric likelihoods PhD Diss., Dep. Stat., Univ. Ga., Athens
  37. Kim JK. 2009. Calibration estimation using empirical likelihood in survey sampling. Stat. Sin. 19:145–57
    [Google Scholar]
  38. Kitamura Y. 1997. Empirical likelihood methods with weakly dependent processes. Ann. Stat. 25:2084–102
    [Google Scholar]
  39. Kleiner A, Talwalkar A, Sarkar P, Jordan MI 2014. A scalable bootstrap for massive data. J. R. Stat. Soc. Ser. B 76:795–816
    [Google Scholar]
  40. Kolaczyk ED. 1994. Empirical likelihood for generalized linear models. Stat. Sin. 4:199–218
    [Google Scholar]
  41. Lazar NA. 2003. Bayesian empirical likelihood. Biometrika 90:319–26
    [Google Scholar]
  42. Lazar NA, Mykland PA. 1999. Empirical likelihood in the presence of nuisance parameters. Biometrika 86:203–11
    [Google Scholar]
  43. Lindsay B. 1988. Composite likelihood methods. Contemp. Math. 80:220–39
    [Google Scholar]
  44. Molanes-Lopez E, Van Keilegom I, Veraverbeke N 2009. Empirical likelihood for non-smooth criterion functions. Scand. J. Stat. 36:413–32
    [Google Scholar]
  45. Monahan JF, Boos DD. 1992. Proper likelihoods for Bayesian analysis. Biometrika 79:271–78
    [Google Scholar]
  46. Mykland PA. 1995. Dual likelihood. Ann. Stat. 23:396–421
    [Google Scholar]
  47. Neal RM. 2011. MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo S Brooks, A Gelman, GL Jones, XL Meng 113–62 Boca Raton, FL: Chapman and Hall/CRC
    [Google Scholar]
  48. Neyman J, Pearson ES. 1928a. On the use and interpretation of certain test criteria for purposes of statistical inference. Part I. Biometrika 20A:175–240
    [Google Scholar]
  49. Neyman J, Pearson ES. 1928b. On the use and interpretation of certain test criteria for purposes of statistical inference. Part II. Biometrika 20A:263–94
    [Google Scholar]
  50. Neyman J, Pearson ES. 1933. On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. Lond. Ser. A 231:289–337
    [Google Scholar]
  51. Nordman DJ, Lahiri SN. 2006. A frequency domain empirical likelihood for short- and long-range dependence. Ann. Stat. 34:3019–50
    [Google Scholar]
  52. Nordman DJ, Lahiri SN. 2014. A review of empirical likelihood methods for time series. J. Stat. Plan. Inference 155:1–18
    [Google Scholar]
  53. Oguz-Alper M, Berger YG. 2016. Modelling complex survey data with population level information: an empirical likelihood approach. Biometrika 103:447–59
    [Google Scholar]
  54. Owen AB. 1988. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–49
    [Google Scholar]
  55. Owen AB. 1990. Empirical likelihood ratio confidence regions. Ann. Stat. 18:90–120
    [Google Scholar]
  56. Owen AB. 1991. Empirical likelihood for linear models. Ann. Stat. 19:1725–47
    [Google Scholar]
  57. Owen AB. 2001. Empirical Likelihood Boca Raton, FL: Chapman and Hall/CRC
  58. Pan XR, Zhou M. 2002. Empirical likelihood ratio in terms of cumulative hazard function for censored data. J. Multivar. Anal. 80:166–88
    [Google Scholar]
  59. Qin J, Lawless J. 1994. Empirical likelihood and general estimating equations. Ann. Stat. 22:300–25
    [Google Scholar]
  60. book 2017. R: a language and environment for statistical computing. Statistical Software R Found. Stat. Comput Vienna:
    [Google Scholar]
  61. Rubin D. 1981. The Bayesian bootstrap. Ann. Stat. 9:130–34
    [Google Scholar]
  62. Schennach SM. 2005. Bayesian exponentially tilted empirical likelihood. Biometrika 92:31–46
    [Google Scholar]
  63. Shi J, Lau TS. 2000. Empirical likelihood for partially linear models. J. Multivar. Anal. 72:132–48
    [Google Scholar]
  64. Stigler SM. 2007. The epic story of maximum likelihood. Stat. Sci. 22:598–620
    [Google Scholar]
  65. Tang CY, Leng C. 2010. Penalized high-dimensional empirical likelihood. Biometrika 97:905–20
    [Google Scholar]
  66. Wang Q, Rao JNK. 2002. Empirical likelihood-based inference in linear models with missing data. Scand. J. Stat. 29:563–76
    [Google Scholar]
  67. Wang QH, Jing BY. 2003. Empirical likelihood for partial linear models. Ann. Inst. Stat. Math. 55:585–95
    [Google Scholar]
  68. Wedderburn RWM. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61:439–47
    [Google Scholar]
  69. Wilks SS. 1938. The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9:60–62
    [Google Scholar]
  70. Xue L. 2009. Empirical likelihood for linear models with missing responses. J. Multivar. Anal. 100:1353–66
    [Google Scholar]
  71. Yang D, Small DS. 2013. An R package and a study of methods for computing empirical likelihood. J. Stat. Comput. Simul. 83:1363–72
    [Google Scholar]
  72. Zhao P, Wu C. 2019. Some theoretical and practical aspects of empirical likelihood methods for complex surveys. Int. Stat. Rev. 87:S1S239–56
    [Google Scholar]
  73. Zhou M. 2015. Empirical Likelihood Method in Survival Analysis Boca Raton, FL: Chapman and Hall/CRC
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