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LINEAR MODELS AND ANALYSIS

Rate of Strong Consistency of Maximum Quasi-Likelihood Estimator in Multivariate Generalized Linear Models

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Pages 3115-3123 | Received 31 Aug 2007, Accepted 24 Mar 2008, Published online: 15 Aug 2008

References

  • Andersen , P. K. , Borgan , O. , Gill , R. , Keiding , N. ( 1993 ). Statistical Models Based on Counting Processes . New York : Spring-Verlag .
  • Chang , Y. C. I. ( 1999 ). Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time . Statist. Probab. Lett. 45 : 237 – 246 .
  • Chen , K. N. , Hu , I. C. , Ying , Z. L. ( 1999 ). Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs . Ann. Statist. 27 : 1155 – 1163 .
  • Dugundji , J. ( 1966 ). Topology . Boston : Allyn and Bacon .
  • Fahrmeir , L. ( 1990 ). Maximum likelihood estimation in misspecified generalized linear models . Statistics 21 : 487 – 502 .
  • Fahrmeir , L. , Kanfmann , H. ( 1985 ). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models . Ann. Statist. 13 : 342 – 368 .
  • Fan , J. , Gijbels , I. ( 1996 ). Local Polynomial Modelling and Its Applications . London : Chapman & Hall .
  • Finney , D. J. (1978). Statistical Method in Biological Assay . London : Griffin.
  • Hall , P. , Heyde , C. C. ( 1980 ). Martingale Limit Theory and its Application . New York : Academic Press .
  • Heuser , H. ( 1981 ). Lehrbuch der Analysis, Teil 2 . Stuttgart : Teubner .
  • Lai , T. L. , Robbins , H. ( 1979 ). Adaptive design and stochastic approximation . Ann. Statist. 7 : 1196 – 1221 .
  • Liang , K. Y. , Zeger , S. L. ( 1986 ). Longitudinal data analysis using generalized linear models . Biometrika 73 : 13 – 22 .
  • Nelder , J. A. , Wedderburn , R. W. M. ( 1972 ). Generalized linear models . J. Roy. Statist. Soc. Ser. A 135 : 370 – 384 .
  • Wedderburn , R. W. M. ( 1974 ). Quasi-likelihood functions, generalized linear models, and the Gauss–Newton method . Biometrika 61 : 439 – 447 .
  • Wetherill , G. B. ( 1963 ). Sequential estimation of quantal response curves (with discussion) . J. Roy. Statist. Soc. Ser. B 25 : 1 – 48 .
  • Wu , C. F. J. ( 1985 ). Efficient sequential designs with binary data . J. Amer. Statist. Assoc. 80 : 974 – 984 .
  • Wu , C. F. J. ( 1986 ). Maximum likelihood recursion and stochastic approximation in sequential designs . In : Van Ryzen , J. , ed. Adaptive Statistical Procedures and Related Topics . Vol. 8 . AMS Monograph Series . Hayward , CA : Institute of Mathematical Statistics , pp. 298 – 313 .
  • Yin , C. H. , Zhao , L. C. , Wei , C. D. ( 2006 ). Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models . Sci. China, Ser. A 48 : 145 – 157 .
  • Yue , L. , Chen , X. R. ( 2004 ). Rates of a.s. convergence of the maximum quasi-likelihood estimator in generalized linear models . Sci. China, Ser. A 47 : 882 – 893 .
  • Yue , L. , Chen , X. R. ( 2005 ). Asymptotic normality of quasi-likelihood estimates in generalized linear models . Chin. Ann. Math., Ser. B 26 : 467 – 474 .
  • Zeger , S. L. , Liang , K. Y. ( 1986 ). Longitudinal data analysis for discrete and continuous outcomes . Biometrics 42 : 121 – 130 .

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