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The Loss of Efficiency Estimating Linear Functions under Restrictions

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  • Miguel A. Fernandez
  • Cristina Rueda
  • Bonifacio Salvador

Abstract

This article is motivated by the problem of estimating contrast in a one‐way ANOVA model with restrictions in the parameter vector. We prove that when the restrictions are given by a tree order or a simple order the MLE of some contrast has greater MSE than the unrestricted estimator. A similar behaviour of the MLE is exhibited in a general restricted setting given by a multivariate normal distribution with mean vector constrained to belong to a circular cone. The approach we use focuses on the central direction of the cones. These directions appear to have the greater MSE when the dimension of the restricted cone is big enough.

Suggested Citation

  • Miguel A. Fernandez & Cristina Rueda & Bonifacio Salvador, 1999. "The Loss of Efficiency Estimating Linear Functions under Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 579-592, December.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:4:p:579-592
    DOI: 10.1111/1467-9469.00169
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    Cited by:

    1. Yuan-Tsung Chang & Nobuo Shinozaki, 2002. "A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 848-860, December.

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