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Elements of Large-Sample Theory

  • William E. Strawderman
  • Erich L. Lehmann
  • Susan P. Holmes
Open Access
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Abstract

This introductory book on the most useful parts of large-sample theory is designed to be accessible to scientists outside statistics and certainly to master’s-level statistics students who ignore most of measure theory. According to the author, “the subject of this book, first-order large- sample theory, constitutes a coherent body of concepts and results that are central to both theoretical and applied statistics.” All of the other existing books published on the subject over the last 20 years, from Ibragimov and Has’minskii in 1979 to the most recent by Van der Waart in 1998 have a common prerequisite in mathematical sophistication (measure theory in particular) that do not make the concepts available to a wide audience.

Keywords

Measure Theory American Statistical Association Nonparametric Estimation Triangular Array Asymptotic Optimality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Casella, G., and Berger, R. L. (1990), Statistical Inference, Pacific Grove, CA: Wadsworth.MATHGoogle Scholar
  2. Ferguson, T. S. (1996), A Course in Large-Sample Theory, London: Chapman and Hall.MATHGoogle Scholar
  3. Glick, N. (1972), “Sample-Based Classification Procedures Derived From Density Estimators,” Journal of the American Statistical Association, 67, 116–122.MATHCrossRefGoogle Scholar
  4. Ibragimov, I. A., and Has’minskii, R. Z. (1981), Statistical Estimation, New York: Springer-Verlag.MATHGoogle Scholar
  5. Lehmann, E. L. (1975), Nonparametrics, San Francisco: Holden-Day.MATHGoogle Scholar
  6. Lehmann, E. L. (1983), Theory of Point Estimation, London: Chapman and Hall.MATHGoogle Scholar
  7. Lehmann, E. L. (1986), Testing Statistical Hypotheses (2nd ed.), London: Chapman and Hall.MATHGoogle Scholar
  8. Lehmann, E. L., and Casella, G. (1998), Theory of Point Estimation (2nd ed.), New York: Springer-Verlag.MATHGoogle Scholar
  9. Van der Vaart, A. (1998), Asymptotic Statistics, Cambridge, U.K.: Cambridge University Press.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • William E. Strawderman
    • 1
  • Erich L. Lehmann
  • Susan P. Holmes
    • 2
  1. 1.Rutgers UniversityRutgersUSA
  2. 2.Stanford UniversityStanfordUSA

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