By Ludwig Fahrmeir, Brian Francis, Robert Gilchrist, Gerhard Tutz
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Additional info for Advances in GLIM and Statistical Modelling: Proceedings of the GLIM92 Conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July 1992
Monfort, A. and Trognon, A. (1984), ''Pseudo Maximum Likelihood Methods: Theory", Econometrica, 52, 681- 700. K. (1962), "On the Solution of the Likelihood Equation by Iteration Processes - The Multiparametric Case" , Biometrika, 48, 452-456. J. and Gentle, I. E. (1980), Statistical Computing, New Yorl< and Basel: Marcel Dekker. McCullagh, P. A. , New Vorl<: Chapman and Hall. Pregibon, D. (1981), 'Logistic Regression Diagnostics", Annals of Statistics, 9, 705-724. M. (1974), "Quasi-Likelihood-Functions, Generalized Linear Models and the Gauss-NewtonMethod", Biometrika, 61, 439-447.
Note that the distribution of the likelihood distance statistic is not known. To find the asymptotic distribution of LDi, one would have to consider the jOint asymptotic distribution of both estimators. This likelihood approach is generalized to PML and QOPML estimation. The likelihood distance statistic depends on the existence of a properly chosen loglikelihood function. If the likelihood function is replaced by the pseudo likelihood function one should use the likelihood distance of the assumed likelihood function only if the conditionA(#o) = -B(#o) is fulfilled: In the general case, where the assumed density is not of the form of the true conditional density of y given x the likelihood distance must be replaced by a statistic that is asymptotically equivalent to LDi if A(#o) = -B(#o), but is robust against violations of this condition.
Fuller, editors. American Mathematics Society, Providence. Kiichenhoff, H. (1990). Logit- und Probitregression mit Fehlen in den Variabeln. Anton Hain, Frankfurt am Main. Li, KC. (1991). Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86, 316-342. Liang, K Y. & Liu, X. H. (1991). Estimating equations in generalized linear models with measurement error. In Estimating Functions, V. P. Godambe, editor. Clarendon Press, Oxford. Nakamura, T.
Advances in GLIM and Statistical Modelling: Proceedings of the GLIM92 Conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July 1992 by Ludwig Fahrmeir, Brian Francis, Robert Gilchrist, Gerhard Tutz