Advertisement

Estimating equations

  • Bing LiEmail author
  • G. Jogesh Babu
Chapter
  • 2k Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

The theory of estimating equations is developed in this chapter. Estimating equations are a generalization of the maximum likelihood method and the method of moments, and have their combined flavors and advantages. Estimating equations are the basic components for Quasi Likelihood, Generalized Linear Models, Generalized Estimating Equations, and Generalized Method of Moments, which have wide applications. In addition, estimating equations also provide a convenient theoretical framework to develop many aspects of statistical inference, such as conditional inference, inference in the presence of nuisance parameters, efficient estimation, and the information bounds. They make some optimal results in statistical inference transparent via projections in Hilbert spaces.

References

  1. Bhattacharyya, A. (1946). On some analogues of the amount of information and their use in statistical estimation. Sankhya: The Indian Journal of Statistics. 8, 1–14.Google Scholar
  2. Bickel, P. J., Klaassen, C. A. J., Ritov, Y. Wellner, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. The Johns Hopkins University Press.Google Scholar
  3. Cox, D. R. and Hinkley, D. (1974). Theoretical Statistics. Chapman & Hall.Google Scholar
  4. Crowder, M. (1987). On linear and quadratic estimating functions. Biometrika, 74, 591–597.MathSciNetCrossRefGoogle Scholar
  5. Durbin, J. (1960). Estimation of parameters in time-series regression models. Journal of the Royal Statistical Society, Series B, 22, 139–153.MathSciNetzbMATHGoogle Scholar
  6. Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics, 31, 1208–1211.MathSciNetCrossRefGoogle Scholar
  7. Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations. Biometrikca, 63, 277–284.MathSciNetCrossRefGoogle Scholar
  8. Godambe, V. P. and Thompson, M. E. (1989). An extension of quasi-likelihood estimation. Journal of Statistical Planning and Inference, 22, 137–152.MathSciNetCrossRefGoogle Scholar
  9. Hansen, L. P. (1982). Large sample properties of Generalized Method of Moments Estimators. Econometrica, 50, 1029–1054.MathSciNetCrossRefGoogle Scholar
  10. Heyde, C. C. (1997). Quasi-Likelihood and its Application: a General Approach to Optimal Parameter Estimation. Springer.Google Scholar
  11. Jarrett, R. G. (1984). Bounds and expansions for Fisher information when the moments are known. Biometrika, 71, 101–113.MathSciNetCrossRefGoogle Scholar
  12. Li, B. (1993). A deviance function for the quasi-likelihood method. Biometrika, 80, 741–753.MathSciNetCrossRefGoogle Scholar
  13. Li, B. (1996). A minimax approach to consistency and efficiency for estimating equations. The Annals of Statistics, 24, 1283–1297.MathSciNetCrossRefGoogle Scholar
  14. Li, B. and McCullagh, P. (1994). Potential functions and conservative estimating functions. The Annals of Statistics, 22, 340–356.MathSciNetCrossRefGoogle Scholar
  15. Liang, K. Y. and Zeger, S. L. (1986). Longitutinal data analysis using generalized linear models. Biometrika, 73, 13–22.MathSciNetCrossRefGoogle Scholar
  16. Lindsay, B. (1982). Conditional score functions: some optimality results. Biometrika, 69, 503–512.MathSciNetCrossRefGoogle Scholar
  17. McCullagh, P. (1983). Quasi-likelihood functions. The Annals of Statistics, 11, 59–67.MathSciNetCrossRefGoogle Scholar
  18. Morton, R. (1981). Efficiency of estimating equations and the use of pivots. Biometrika, 68, 227–233.MathSciNetCrossRefGoogle Scholar
  19. Small, C. G. and McLeish, D. L. (1989). Projection as a method for increasing sensitivity and eliminating nuisance parameters. Biometrika, 76, 693–703.MathSciNetCrossRefGoogle Scholar
  20. Waterman, R. P and Lindsay, B. G. (1996). Projected score methods for approximating conditional scores. Biometrika, 83, 1–13.MathSciNetCrossRefGoogle Scholar
  21. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, Generalized Linear Models, and the Gauss-Newton method. Biometrika, 61, 439–447.MathSciNetzbMATHGoogle Scholar
  22. Zeger, S. L. and Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42, 121–130.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsPenn State UniversityUniversity ParkUSA

Personalised recommendations