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I-projection onto isotonic cones and its applications to maximum likelihood estimation for log-linear models

  • Order Restricted Inference
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Abstract

A frequently occurring problem is to find a probability vector,p∈D, which minimizes theI-divergence between it and a given probability vector π. This is referred to as theI-projection of π ontoD. Darroch and Ratcliff (1972,Ann. Math. Statist.,43, 1470–1480) gave an algorithm whenD is defined by some linear equalities and in this paper, for simplicity of exposition, we propose an iterative procedure whenD is defined by some linear inequalities. We also discuss the relationship betweenI-projection and the maximum likelihood estimation for multinomial distribution. All of the results can be applied to isotonic cone.

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Authors and Affiliations

  1. Department of Mathematics, Northeast Normal University, Changchun, 130024, China

    Wei Gao & Ning-Zhong Shi

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan

    Wei Gao

Authors
  1. Wei Gao
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  2. Ning-Zhong Shi
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Gao, W., Shi, NZ. I-projection onto isotonic cones and its applications to maximum likelihood estimation for log-linear models. Ann Inst Stat Math 55, 251–263 (2003). https://doi.org/10.1007/BF02530498

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  • DOI: https://doi.org/10.1007/BF02530498

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