Robust Moment Based Estimation and Inference: The Generalized Cressie-Read Estimator


In this paper a range of information theoretic distance measures, based on Cressie-Read divergence, are combined with mean-zero estimating equations to provide an efficient basis for semi parametric estimation and testing. Asymptotic properties of the resulting semi parametric estimators are demonstrated and issues of implementation are considered.


Empirical Likelihood Reference Distribution Empirical Likelihood Ratio Extremum Metrics Semi Parametric Estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baggerly, K.: Empirical likelihood as a goodness of fit measure. Biometrika 85, 535–547 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baggerly, K.: Studentized empirical likelihood and maximum entropy empirical t. Working paper, Department of Statistics, Rice University, Houston, Texas (2001)Google Scholar
  3. 3.
    Brown, B., Chen, S.: Combined least squares empirical likelihood. Ann. Inst. Stat. Math. 60, 697–714 (1998)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Corcoran, S.: Empirical exponential family likelihood using several moment conditions. Stat. Sinica 10, 545–557 (2000)MATHGoogle Scholar
  5. 5.
    Cotofrei, P.: A possible generalization of the empirical likelihood computer sciences. Technical report, University of “A.I. Cuza,” Iasi, Romania (2003)Google Scholar
  6. 6.
    Cressie, N., Read, T.: Multinomial goodness of fit tests. J. Roy. Statist. Soc. B 46, 440–464 (1984)MATHMathSciNetGoogle Scholar
  7. 7.
    Golan, A., Judge, G.G., Miller, D.: Maximum Entropy Econometrics. Wiley, New York. (1996)MATHGoogle Scholar
  8. 8.
    Godambe, V.: An optimum property of regular maximum likelihood estimation. Ann. Math. Stat. 31, 1208–1212 (1960)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Grunwald, P., David, A.: Game theory, maximum entropy, minimum discrepancy and robust bayesian decision theory. Ann. Stat. 32, 1367–1433 (2004)CrossRefGoogle Scholar
  10. 10.
    Judge, G.G., Griffith, W.E., Hill, R.C., Lütkepohl, H., Lee, T.-C.: The Theory and Practice of Econometrics. Wiley, New York. (1985)Google Scholar
  11. 11.
    Imbens, G.W., Spady, R.H., Johnson, P.: Information theoretic approaches to inference in moment condition models. Econometrica 66, 333–357 (1998)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hansen, L.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054 (1982)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Heyde, C.: Quasilikelihood and optimality of estimating functions: some current and unifying themes. Bull. Int. Stat. Inst. 1, 19–29 (1989)MathSciNetGoogle Scholar
  14. 14.
    Heyde, C., Morton, R.: Multiple roots in general estimating equations. Biometrika 85, 954–959 (1998)MATHCrossRefGoogle Scholar
  15. 15.
    Lindsay, B., Qu, A.: Inference functions and quadratic score tests. Stat. Sci. 18, 394–410 (2003)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Mittelhammer, R., Judge, G.G.: Robust empirical likelihood estimation of models with nonorthogonal noise components. Volume in Honor of Henri Theil. To appear in: J. Agr. Appl. Econ. (2008)Google Scholar
  17. 17.
    Mittelhammer, R., Judge, G.G.: Endogeneity and Moment Based Estimation under Squared Error Loss. In:Wan, A., Ullah, A. (eds.) Handbook of Applied Econometrics and Statistical Inference, Dekker, New York (2001)Google Scholar
  18. 18.
    Newey, W., Smith, R.: Asymptotic bias and equivalence of GMM and GEL estimators. MIT Working paper, MIT, USA. (2000)Google Scholar
  19. 19.
    Österreicher, F.: Csiszar’s f-divergencies-basic properties. Working paper, Institute of Mathematics, University of Salzburg, Austria. (2002)Google Scholar
  20. 20.
    Österreicher, F., Vajda, I.: A new class of metric divergencies on probability spaces and its applicability in statistics. Ann. Inst. Stat. Math. 55, 639–653 (2003)MATHCrossRefGoogle Scholar
  21. 21.
    Owen, A.: Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237-249 (1988)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Owen, A.: Empirical likelihood for linear models. Ann. Stat. 19, 1725–1747 (1991)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Owen, A.: Empirical Likelihood, Chapman & Hall, New York. (2001)MATHGoogle Scholar
  24. 24.
    Qin, J.: Combining parametric and empirical likelihood data. Biometrika 87, 484–490 (2000)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Qin, J., Lawless, J.: Empirical likelihood and general estimating equations. Ann. Stat. 22, 300–325 (1994)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Mittelhammer, R., Judge, G.G., Miller, D.: Econometric Foundations. Cambridge University Press, Cambridge. (2000)MATHGoogle Scholar
  27. 27.
    Mittelhammer, R., Judge, G.G., Schoenberg, R.: Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods. In: Festschrift in Honor of Thomas Rothenberg, Cambridge University Press, Cambridge, UK. (2003)Google Scholar
  28. 28.
    Rao, C.R.: Tests of significance in multivariate analysis. Biometrika 35, 58–79 (1948)MATHMathSciNetGoogle Scholar
  29. 29.
    Read, T., Cressie, N.: Goodness of fit statistics for discrete multivariate data. Springer, New York (1988)MATHGoogle Scholar
  30. 30.
    Topsoe, F.: Informational theoretical optimization techniques. Kybernetika 15, 8–27 (1979)MathSciNetGoogle Scholar
  31. 31.
    Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, New York. (1991)MATHGoogle Scholar
  32. 32.
    Wolpert, D., Wolf, D.: Estimating functions of probability distributions from a finite set of data. Phys. Rev. E 6, 6841–6852 (1995)CrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.School of Economic SciencesWashington State UniversityPullman
  2. 2.University of California-BerkeleyBerkeley

Personalised recommendations