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Maximum Information and Optimum Estimating Function

Lu Lin

Department of Statistics, School of Mathematical Sciences, Nankai University, Tianjin 300071, China

https://doi.org/10.1142/S0252959903000359Cited by:1 (Source: Crossref)

Abstract

In order to construct estimating functions in some parametric models, this paper introduces two classes of information matrices. Some necessary and sufficient conditions for the information matrices achieving their upper bounds are given. For the problem of estimating the median, some optimum estimating functions based on the information matrices are acquired. Under some regularity conditions, an approach to carrying out the best basis function is introduced. In nonlinear regression models, an optimum estimating function based on the information matrices is obtained. Some examples are given to illustrate the results. Finally, the concept of optimum estimating function and the methods of constructing optimum estimating function are developed in more general statistical models.

Project supported by the National Natural Science Foundation of China (No.10171051) and the Youth Teacher Foundation of Nankai University.

Document Code: A, Article ID: 0252-9599(2003)03-0349-10

Keywords:

References

A. Birnbaum, Journal of Mathematical Psychology 37, 29 (1972). Google Scholar
V. P. Godambe and C. D. Heyde, Internat Statist. Rev. 55, 231 (1987), DOI: 10.2307/1403403. Crossref, Google Scholar
V. P. Godambe and M. E. Thompson, J. Statist. Plan. Inference 22, 137 (1989), DOI: 10.1016/0378-3758(89)90106-7. Crossref, Google Scholar
V. P. Godambe and M. E. Thompson, Biometrika 71, 115 (1984), DOI: 10.1093/biomet/71.1.115. Crossref, Google Scholar
Godambe, V. P., Estimation of method: quasi-likelihood and optimum estimating function, Working Paper, 2001-04, Department of Statistics and Actuarial Science University of Waterloo, 2001 . Google Scholar
S. Jung, JASA 91, 251 (1996). Crossref, Google Scholar
B. Li and P. McCullagh, Annals of Statistics 22, 341 (1994), DOI: 10.1214/aos/1176325372. Google Scholar
L. Lin, Mathematica Acta Sinientia 20(3), 335 (2000). Crossref, Google Scholar
L. Lin, Acta Mathematicae Applicatae Sinica 22(2), 307 (1999). Google Scholar
P. McCullagh, Annals of Statistics 11, 59 (1983), DOI: 10.1214/aos/1176346056. Crossref, Google Scholar
P. McCullagh and J. A. Nelder, Generalized linear models, 2nd edn. (Chapman and Hall, London, 1989) pp. 323–339. Crossref, Google Scholar
R. W. M. Wedderburn, Biometrika 61, 439 (1974). Google Scholar