MONOTONICITY OF QUADRATIC-APPROXIMATION ALGORITHMS
MONOTONICITY OF QUADRATIC-APPROXIMATION ALGORITHMS
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DOI：
10.1007/bf00049423
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发表时间：
1988-01-01
影响因子：
1
通讯作者：
LINDSAY, BG
中科院分区：
文献类型：
--
作者：
BOHNING, D;LINDSAY, BG
为了保证算法的收敛稳定性，最大化算法的目标函数是单调递增的。它在这里示出了如何可以调整牛顿-拉夫逊过程，以达到单调性的目标函数的曲率上使用简单的界限。分析中的基本工具是通过将二次近似算法解释为面积近似的形式而获得的几何洞察力。讨论的统计实例包括混合模型中的最大似然估计、逻辑回归和考克斯比例风险回归。
It is desirable that a numerical maximization algorithm monotonically increase its objective function for the sake of its stability of convergence. It is here shown how one can adjust the Newton-Raphson procedure to attain monotonicity by the use of simple bounds on the curvature of the objective function. The fundamental tool in the analysis is the geometric insight one gains by interpreting quadratic-approximation algorithms as a form of area approximation. The statistical examples discussed include maximum likelihood estimation in mixture models, logistic regression and Cox's proportional hazards regression.