Abstract
The lower bound principle (introduced in Böhning and Lindsay 1988, Ann. Inst. Statist. Math., 40, 641–663), Böhning (1989, Biometrika, 76, 375–383) consists of replacing the second derivative matrix by a global lower bound in the Loewner ordering. This bound is used in the Newton-Raphson iteration instead of the Hessian matrix leading to a monotonically converging sequence of iterates. Here, we apply this principle to the multinomial logistic regression model, where it becomes specifically attractive.
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References
Baksalary, J. K. and Pukelsheim, F. (1985). A note on the matrix ordering of special C-matrices, Linear Algebra Appl., 70, 263–267.
Böhning, D. (1989). Likelihood inference for mixtures: Geometrical and other constructions of monotone step-length algorithms, Biometrika, 76, 375–383.
Böhning, D. and Lindsay, B. (1988). Monotonicity of quadratic-approximation algorithms, Ann. Inst. Statist. Math., 40, 641–663.
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Supplement to “Monotonicity of quadratic-approximation algorithms” by Böhning and Lindsay (1988). Ann. Inst. Statist. Math., 40, 641–663.
This research was supported by the German Research Foundation.
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Böhning, D. Multinomial logistic regression algorithm. Ann Inst Stat Math 44, 197–200 (1992). https://doi.org/10.1007/BF00048682
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DOI: https://doi.org/10.1007/BF00048682