Convergence Rate of Strong Consistency of the Maximum Likelihood Estimator in Exponential Family Nonlinear Models

References

• Bennett , G. ( 1962 ). Probability inequality for sums of independent random variables . J. Amer. Statist. Assoc. 57 : 33 – 45 .
   Web of Science ®Google Scholar
• Cook , R. D. , Tsai , C. L. ( 1990 ). Diagnostics for assessing the accuracy of normal approximations in exponential family nonlinear models . J. Amer. Statist. Assoc. 85 : 770 – 777 .
   Web of Science ®Google Scholar
• Cordeiro , G. M. , Paula , G. A. ( 1989 ). Improved likelihood ratio statistics for exponential family nonlinear models . Biometrika 76 : 93 – 100 .
   Web of Science ®Google Scholar
• Fahrmeir , L. , Kaufmann , H. ( 1985 ). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models . Ann. Statist. 13 : 342 – 368 .
   Web of Science ®Google Scholar
• Jennrich , R. I. (1969). Asymptotic properties of nonlinear least squares estimators. Ann. Math. Statist. 40:633–643.
   Google Scholar
• Malinvaud , E. ( 1970 ). The consistency of nonlinear regression . Ann. Statist. 41 : 956 – 969 .
   Google Scholar
• Nelder , J. A. , Wedderburn , R. W. M. ( 1972 ). Generalized linear models . J. R. Statist. Soc. A. 135 : 370 – 384 .
   Web of Science ®Google Scholar
• Pazman , A. ( 1991 ). Curvatures and the distribution of the maximum likelihood estimator in nonlinear exponential models . Brazilian J. Prob. Statist. 5 : 43 – 63 .
   Google Scholar
• Petrov , V. V. ( 1975 ). Sums of Independent Random Variables . New York : Springer-Verlag .
   Google Scholar
• Stout , W. F. ( 1974 ). Almost Sure Convergence . New York : Academic Press .
   Google Scholar
• Wei , B. C. ( 1998 ). Exponential Family Nonlinear Models . Singapore : Springer-Verlag , pp. 195 – 209 .
   Google Scholar
• Wu , C. F. ( 1981 ). Asymptotic theory of nonlinear least squares estimation . Ann. Statist. 9 : 501 – 513 .
   Web of Science ®Google Scholar
• Yue , L. , Chen , X. R. ( 2004 ). Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models . Sci. China Ser. A. Math. 47 : 882 – 893 .
   Google Scholar