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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Multivariate Limited Translation Hierarchical Bayes Estimators.

Malay Ghosh1, Georgios Papageorgiou, Janet Forrester

  • 1University of Florida, Department of Statistics, 103 Griffin/Floyd Hall - P.O. Box 118545, Gainesville, FL 32611-8545.

Journal of Multivariate Analysis
|July 22, 2011
PubMed
Summary

This study introduces new hierarchical Bayes estimators for normal mean vectors, offering a balance between existing methods. These estimators show improved performance when true parameters significantly differ from the average.

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Area of Science:

  • Statistics
  • Statistical Inference

Background:

  • Hierarchical Bayes (HB) and Maximum Likelihood (ML) estimators are standard for normal mean vector estimation.
  • Existing HB estimators can be sensitive to deviations from the grand mean.
  • Limited translation methods offer a potential improvement by balancing bias and variance.

Purpose of the Study:

  • To develop multivariate limited translation hierarchical Bayes estimators for the normal mean vector.
  • To provide a compromise between traditional HB and ML estimators.
  • To evaluate the frequentist risks of these new estimators compared to standard HB estimators.

Main Methods:

  • Utilizing the concept of predictive influence functions.
  • Developing multivariate limited translation hierarchical Bayes (HB) estimators.
  • Comparing frequentist risks of limited translation HB estimators against standard HB estimators.

Main Results:

  • The proposed limited translation HB estimators offer a compromise between HB and ML estimators.
  • These estimators demonstrate superior frequentist risk performance compared to standard HB estimators.
  • Superiority is particularly evident when the true parameter vector deviates substantially from the grand mean.

Conclusions:

  • Multivariate limited translation HB estimators provide a robust alternative for normal mean vector estimation.
  • The predictive influence function approach is effective for developing improved statistical estimators.
  • These estimators mitigate issues associated with standard HB methods when parameters are widely dispersed.