(Received July 23, 1990; revised October 12, 1990)
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.
Key words and phrases: Kronecker product, Loewner ordering, lower bound principle, monotonicity.
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