Unbiased Estimation in Convex Families

  • P. J. Bickel
  • E. L. Lehmann
Open Access
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Introduction and summary

Suppose that we observe random variables X 1, • • •, X n which are identically and independently distributed according to some distribution F where F ranges over a family ℱ.

Keywords

Bredon 

References

  1. Ghosh, J. K. and Singh, R. (1966). Unbiased estimation of location and scale param-eters. Ann. Math. Statist. 37 1671–1675.MathSciNetMATHCrossRefGoogle Scholar
  2. Halmos, P. R. (1946). The theory of unbiased estimation. Ann. Math. Statist. 17 34–43.MathSciNetMATHCrossRefGoogle Scholar
  3. Hille, E. and Phillips, R. S. (1957). Functional analysis and semi-groups. Amer.Math. Soc. ColLPubl. 31. Google Scholar
  4. Lehmann, E. L. and Scheffé, Henry (1950). Completeness, similar regions and un-biased estimation. Sankhyā 10 305–340.MATHGoogle Scholar
  5. Renyi, A. (1953). Neue Kriterien zum Vergleich Zweier Stichproben. Magyar Tud. Akad. Mat. Fiz. Oszt. Közl.2 243–265.MathSciNetGoogle Scholar
  6. Rosenblatt, Murray (1956). Remark on some nonparametric estimates of a density function. Ann. Math. Statist. 27 832–837.MathSciNetMATHCrossRefGoogle Scholar
  7. STEFFENSEN, J. (1930). Some Recent Researches in the Theory of Statistics and Actuarial Science. Cambridge Univ. Press.Google Scholar
  8. Trèves, J. F. (1967). Topological Vector Spaces, Distributions, and Kernels. Academic Press, New York.MATHGoogle Scholar
  9. Tukey, John W. (1960). A survey of sampling from contaminated distributions. Contributions to Probability and Statistics. Stanford Univ. Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • P. J. Bickel
    • 1
  • E. L. Lehmann
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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