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An alternating iterative method and its application in statistical inference

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Abstract

This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. (Biometrika, 72, 465–472 (1983)), Shi N. Z. (J. Multivariate Anal., 50, 282–293 (1994)) and El Barmi H. and Dykstra R. (Ann. Statist., 26, 1878–1893 (1998)).

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Authors and Affiliations

  1. Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China

    Ning Zhong Shi & Guo Rong Hu

  2. Department of Basic Courses, Shijiazhuang Railway Institute, Shijiazhuang, 050043, P. R. China

    Qing Cui

Authors
  1. Ning Zhong Shi
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  2. Guo Rong Hu
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  3. Qing Cui
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Corresponding author

Correspondence to Ning Zhong Shi.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 10431010, 10501005) and Science Foundation for Young Teachers of NENU (No. 20070103)

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Shi, N.Z., Hu, G.R. & Cui, Q. An alternating iterative method and its application in statistical inference. Acta. Math. Sin.-English Ser. 24, 843–856 (2008). https://doi.org/10.1007/s10114-007-1017-6

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  • DOI: https://doi.org/10.1007/s10114-007-1017-6

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