A definition of estimator efficiency ink-parameter case

  • J. Tiago de Oliveira
Article
  • 11 Downloads

Summary

The paper introduces a new definition of efficiency in the multiparameter case (θ1,...,θk) when the variance-covariance matrix of the vector estimator (t 1, ...t k) exists. The definition is also applicable to the asymptotically unbiased estimators.

The basic idea is that, as we want in general to estimate some function g(θ1,...θk) of the parameters, efficiency of the vector estimator shall be defined as the smallest efficiency of the estimatorg(t 1, ...t k),g being regular. It is shown that this definition is asymptotically equivalent to the one obtained by any linear combination of the estimators, as it happens, naturally, for quantile estimation in the location-dispersion case. This efficiency is larger than Cramér efficiency which is, thus, not attained, apart from a very exceptional case.

Finally, a lower bound for the asymptotic variance is obtained.

Key words

Multidimensional parameters and estimators functions of parameters and estimators asymptotic unbiasedness variance-covariance matrices efficiency lower bound of the variance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cramér, H. (1946).Mathematical Methods of Statistics, Princeton University Press.Google Scholar
  2. [2]
    Kendall, M. G. and Stuart, A. (1961).The Advanced Theory of Statistics, 2nd vol., 3rd ed., Griffin and Cy., London.Google Scholar
  3. [3]
    Miller, Rupert G. (1974). The jacknife—a review.Biometrika,61, 1–15.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Rao, C. R. (1973).Linear Statistical Inference and its Applications, Wiley, New York.MATHGoogle Scholar
  5. [5]
    Tiago de Oliveira, J. (1972). Statistics for Gumbel and Frechet distributions,International Conference on Structural Safety and Reliabiliy (ed. A. M. Freudenthal), Pergamon Press, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 1982

Authors and Affiliations

  • J. Tiago de Oliveira
    • 1
  1. 1.Academy of Sciences of LisbonLisbonPortugal

Personalised recommendations