Unbiased Range-Preserving Estimators

  • Wassily Hoeffding
Part of the Springer Series in Statistics book series (SSS)

Abstract

An estimator is said to be range-preserving if its values are confined to the range of what it is to estimate. The property of being range-preserving Is an essential property of an estimator, a sine qua non. Other properties, such as unbiasedness, may be desirable in some situations, but an unbiased estimator that Is not range-preserving should be ruled out as an estimator. (We are not speaking of uses of estimators for purposes other than estimation, for example, as test statistics.)

Keywords

Covariance Hull Sine 

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References

  1. Halmos, Paul R. (1946), “The Theory of Unbiased Estimation,” Annals of Mathematical Statistics, 17, 34–43.MathSciNetMATHCrossRefGoogle Scholar
  2. Hartung, Joachim (1981), “Nonnegative Minimum Biased Invariant Estimation in Variance Component Models,” Annals of Statistics, 9, 278–292.MathSciNetMATHCrossRefGoogle Scholar
  3. La Motte, L.R. (1973), “Non-Negative Quadratic Unbiased Estimation of Variance Components,” Journal of the American Statistical Association, 68, 728–730.MathSciNetCrossRefGoogle Scholar
  4. Lehmann, E. L. (1951), “A General Concept of Unbiasedness,” Annals of Mathematical Statistics, 22, 587–592.MathSciNetMATHCrossRefGoogle Scholar
  5. Pukelsheim, Friedrich (1981), “On the Existence of Unbiased Nonnegative Estimates of Variance Covariance Components,” Annals of Statistics, 9, 293–299.MathSciNetMATHCrossRefGoogle Scholar
  6. Searle, S.R. (1971). Linear Models, New York: Wiley.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Wassily Hoeffding
    • 1
  1. 1.University of North Carolina at Chapel HillUSA

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