Unified generalized iterative scaling and its applications

  • Authors:

  • Wei Gao;Ning-Zhong Shi;Man-Lai Tang;Lianyan Fu;Guoliang Tian

  • Affiliations:

  • Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China;Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China;Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2010

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Abstract

Generalized iterative scaling (GIS) has become a popular method for getting the maximum likelihood estimates for log-linear models. It is basically a sequence of successive I-projections onto sets of probability vectors with some given linear combinations of probability vectors. However, when a sequence of successive I-projections are applied onto some closed and convex sets (e.g., marginal stochastic order), they may not lead to the actual solution. In this manuscript, we present a unified generalized iterative scaling (UGIS) and the convergence of this algorithm to the optimal solution is shown. The relationship between the UGIS and the constrained maximum likelihood estimation for log-linear models is established. Applications to constrained Poisson regression modeling and marginal stochastic order are used to demonstrate the proposed UGIS.