Summary
We consider continuous explanatory variables and a constant to formulate a specific generalized linear model of Nelder and Wedderburn (1972). Maximum likelihood parameter estimation, testing, and prediction problems, similar to those of least squares standard multiple regression, can arise from an ill-conditioned information matrix. Although maximum likelihood parameter estimation is asymptotically unbiased, the construction of asymptotically biased parameter estimates can alleviate the detriments resulting from near-singular information while, in many instances, provide a reduction in asymptotic mean squared error. Three adjustments to maximum likelihood are presented: ridge, principal component and Stein estimators.
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Marx, B.D. (1989). Ill-conditioned Information Matrices and the Generalized Linear Model: an Asymptotically Biased Estimation Approach. In: Decarli, A., Francis, B.J., Gilchrist, R., Seeber, G.U.H. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3680-1_24
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DOI: https://doi.org/10.1007/978-1-4612-3680-1_24
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