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On the inadmissibility of preliminary-test estimators when the loss involves a complexity cost

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Summary

Estimation-preceded-by-testing is studied in the context of estimating the mean vector of a multivariate normal distribution under squared error loss together with a complexity cost. It is shown that although the preliminary test estimator is admissible for the univariate problem (cf Meeden and Arnold (1979),J. Amer. Statist. Assoc.,74, 872–874), for dimensionp≧3, the estimator is inadmissible. A new preliminary test estimator is obtained, which depends on the cost for each component and dominates the usual preliminary test estimator.

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References

  1. Baranchik, A. J. (1970). A family of minimax estimators of the mean of a multivariate normal distribution,Ann. Math. Statist.,41, 642–645.

    Article  MathSciNet  Google Scholar 

  2. Bock, M. E., Yancey T. A. and Judge, G. G. (1972). The statistical consequences of preliminary test estimators in regression,J. Amer. Statist. Assoc.,68, 109–116.

    Article  MathSciNet  Google Scholar 

  3. Brown, L. D. and Hwang, J. T. (1982). A unified admissibility proof. Statistical Decision Theory and Related Topics III, Academic Press, (eds. S. S. Gupta and J. Berger), Vol. I, 205–230.

  4. Faden, A. M. and Rausser, G. C. (1976). Econometric policy model construction: the post-Bayesian approach,Ann. Economic and Social Measurement,5, 349–362.

    Google Scholar 

  5. Meeden, G. and Arnold, B. C. (1979). The admissibility of a preliminary test estimator when the loss incorporates a complexity cost,J. Amer. Statist. Assoc.,74, 872–874.

    Article  MathSciNet  Google Scholar 

  6. Nagata, Y. (1983). Admissibility of some preliminary test estimators for the mean of normal distribution,Ann. Inst. Statist. Math. 35, 365–373.

    Article  MathSciNet  Google Scholar 

  7. Sclove, S. L., Morris, C. and Radhakrishnan, R. (1972). Non optimality of preliminary-test estimators for the mean of a multivariate normal distribution,Ann. Math. Statist.,43, 1481–1490.

    Article  MathSciNet  Google Scholar 

  8. Stein, C. (1981). Estimation of the mean of a multivariate normal distribution,Ann. Statist.,9, 1135–1151.

    Article  MathSciNet  Google Scholar 

  9. Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean,Ann. Math. Statist.,42, 385–388.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Florida, Florida, USA

    Malay Ghosh & Dipak K. Dey

  2. The University of Connecticut, Connecticut, USA

    Malay Ghosh & Dipak K. Dey

Authors
  1. Malay Ghosh
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  2. Dipak K. Dey
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Additional information

Research partially supported by the NSF Grant Number DMS-82-18091 and partially by the DSR Research Development Award, University of Florida.

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Ghosh, M., Dey, D.K. On the inadmissibility of preliminary-test estimators when the loss involves a complexity cost. Ann Inst Stat Math 38, 419–427 (1986). https://doi.org/10.1007/BF02482528

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  • DOI: https://doi.org/10.1007/BF02482528

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