Annals of the Institute of Statistical Mathematics

, Volume 40, Issue 4, pp 641–663

Monotonicity of quadratic-approximation algorithms

  • Dankmar Böhning
  • Bruce G. Lindsay

DOI: 10.1007/BF00049423

Cite this article as:
Böhning, D. & Lindsay, B.G. Ann Inst Stat Math (1988) 40: 641. doi:10.1007/BF00049423


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.

Key words and phrases

Maximum likelihood estimationcurvaturemonotonicityalgorithmsNewton-Raphson algorithm

Copyright information

© The Institute of Statistical Mathematics 1988

Authors and Affiliations

  • Dankmar Böhning
    • 1
  • Bruce G. Lindsay
    • 1
  1. 1.Department of StatisticsThe Pennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.Department of EpidemiologyFreie Universität BerlinBerlin 45Germany