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Unified generalized iterative scaling and its applications

Author

Listed:
  • Gao, Wei
  • Shi, Ning-Zhong
  • Tang, Man-Lai
  • Fu, Lianyan
  • Tian, Guoliang

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.

Suggested Citation

  • Gao, Wei & Shi, Ning-Zhong & Tang, Man-Lai & Fu, Lianyan & Tian, Guoliang, 2010. "Unified generalized iterative scaling and its applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1066-1078, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1066-1078
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    References listed on IDEAS

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    1. Wei Gao & Ning-Zhong Shi, 2003. "I-projection onto isotonic cones and its applications to maximum likelihood estimation for log-linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 251-263, June.
    2. Richard L. Dykstra & Peter C. Wollan, 1987. "Finding I‐Projections Subject to a Finite Set of Linear Inequality Constraints," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 377-383, November.
    3. Bhaskar Bhattacharya & Richard Dykstra, 1997. "A Fenchel Duality Aspect of Iterative I-Projection Procedures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 435-446, September.
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    Cited by:

    1. Xu, Ping-Feng & Sun, Jubo & Shan, Na, 2016. "Local computations of the iterative proportional scaling procedure for hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 17-23.

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