GLOBALLY CONVERGENT ALGORITHMS FOR MAXIMIZING A LIKELIHOOD FUNCTION

• 成果类型: Article
• 署名作者: JENSEN, ST; JOHANSEN, S; LAURITZEN, SL
• 署名单位: Aalborg University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• 发表日期: 1991
• 页码: 867877
• 关键词: regression-models; linear models

摘要

In this paper we show global convergence, under very general assumptions, of iterative maximization procedures with cyclic fixing of groups of parameters, maximizing over the remaining parameters. Further we show that a slightly modified Newton procedure applied to the derivative of the reciprocal likelihood function in a one-dimensional exponential family, is globally convergent. We also prove that if the distribution of the sufficient statistic is infinitely divisible, then the Newton method applied to the derivative of the log likelihood function converges. By combining these results we obtain general globally convergent iterative procedures for maximizing the likelihood function in any regular k-dimensional exponential family. The likelihood function can be maximized either by successively maximizing over one parameter at a time or by maximizing in the Newton direction.