Statistical Science

Decoding the H-likelihood

Xiao-Li Meng

Full-text: Open access

Article information

Source
Statist. Sci. Volume 24, Number 3 (2009), 280-293.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.ss/1270041255

Digital Object Identifier
doi:10.1214/09-STS277C

Mathematical Reviews number (MathSciNet)
MR2757430

Zentralblatt MATH identifier
1329.62340

Keywords
Ancillary statistics Bartlett identities Fisher information Hessian information likelihood principle missing data pivotal predictive distribution prediction posterior predictive distribution random effect

Citation

Meng, Xiao-Li. Decoding the H-likelihood. Statist. Sci. 24 (2009), no. 3, 280--293. doi:10.1214/09-STS277C. https://projecteuclid.org/euclid.ss/1270041255


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References

  • Bayarri, M. J., DeGroot, M. H. and Kadane, J. B. (1988). What is the likelihood function? (with discussion). In Statistical Decision Theory and Related Topics IV (S. S. Gupta and J. O. Berger, eds.). Springer, New York.
  • Berger, J. O. and Robert, L. W. (1988). The Likelihood Principle. IMS, Hayward, CA.
  • Ha, I. D., Lee, Y. and Song, J.-K. (2001). Hierarchical likelihood approach for frailty models. Biometrika 88 233–243.
  • Hannig, J. (2009). On generalized fiducial inference. Statist. Sinica 19 491–544.
  • Hannig, J., Iyer, H. K. and Patterson, P. (2006). Fiducial generalized confidence intervals. J. Amer. Statist. Assoc. 101 254–269.
  • Lee, Y. and Nelder, J. A. (1996). Hierarchical generalised linear models (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 58 619–678.
  • Lee, Y. and Nelder, J. A. (2001). Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika 4 987–1006.
  • Lee, Y. and Nelder, J. A. (2005). Conditional and marginal models: Another view (with discussion). Statist. Sci. 19 219–238.
  • Lee, Y., Nelder, J. A. and Pawitan, Y. (2006). Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood. Chapman and Hall, London.
  • Little, R. J. A. and Rubin, D. B. (1983). On jointly maiximizaing parameters and miss data by maximizing the complete-data likelihood. Amer. Statist. 37 218–220.
  • Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley, New York.
  • Marsden, J. E. and Tromba, A. (2003). Vector Calculus, 5th ed. Freeman, New York.
  • McCullagh, P. (1987). Tensor Methods in Statistics. Chapman and Hall, London.
  • McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
  • Meng, X.-L. (1997). The EM algorithm and medical studies: A historical link. Statistical Methods in Medical Research 6 3–23.
  • Meng, X.-L. (2000). Missing data: Dial M for ??? (A vignette for the Y2K issue). J. Amer. Statist. Assoc. 95 1325–1330. [Also in Statistics in the 21st Century (A. E. Raftery, M. A. Tanner and M. T. Wells, eds.) 397–409. Chapman & Hall/CRC Press, Boca Raton, FL.]
  • Meng, X.-L. (2005). From unit root to Stein estimator to Fisher’s k-statistics: If you have a moment, I can tell you more…. Statist. Sci. 20 141–162.
  • Meng, X.-L. (2008). Who cares if it is a white cat or a black cat? Discussion of “One-step sparse estimates in non-concave penalized likelihood models” by H. Zou and R. Li. Ann. Statist. 36 1542–1552.
  • Mykland, P. A. (1994). Bartlett type identities for martingales. Ann. Statist. 22 21–38.
  • Mykland, P. A. (1999). Bartlett identities and large deviations in likelihood theory. Ann. Statist. 27 1105–1177.
  • Neyman, J. and Scott, E. T. (1948). Consistent estimates based on partially consistent observations. Econometrica 16 1–32.
  • Pearson, K. (1920). The fudenmental problems of practical statistics. Biometrika 13 1–16.
  • Vaida, F. and Meng, X.-L. (2005). Two slice-EM algorithms for fitting generalized linear mixed models with binary response. Stat. Model. 5 229-242.
  • van Dyk, D. A. and Meng, X.-L. (2010). Cross-fertilizing strategies for better EM mountain climbing and DA field exploration: A graphical guide book. Statist. Sci. To appear.