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Weak Convergence for Exponential and Monotone Likelihood Ratio Families and the Convergence of Confidence Limits

  • Bernard Harris
  • Andrew P. Soms
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)

Summary

Two convergence theorems for one-sided confidence limits for exponential and monotone likelehood ratio families are given. In addition, for some special exponential families, the class of discrete limit distributions is characterized and a uniqueness result obtained. Examples of the above results are given. Applications to hypothesis testing and confidence limits are indicated.

Keywords

Weak convergence confidence limits limit distributions exponential family monotone likelihood ratio family 

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References

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    Buehler, R. J. (1957). J. Amer. Statist. Assoc. 52, 482–493.MathSciNetzbMATHCrossRefGoogle Scholar
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    Harris, B. (1971). J. Amer. Statist. Assoc. 66, 609–617.MathSciNetzbMATHCrossRefGoogle Scholar
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    Harris, B. and Soms, A. P. (1974). J. Amer. Statist. Assoc. 69, 259–263.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Harris, B. and Soms, A. P. (1974). Tables of the two factor and three factor generalized incomplete modified Bessel distributions. In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (eds.). Vol. 3. To appear.Google Scholar
  5. [5]
    Hwang, D. (1971). Interval estimation of functions of Bernoulli parameters with reliability and biomedical applications. Technical Report #152, University of Minnesota School of Statistics.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • Bernard Harris
    • 1
  • Andrew P. Soms
    • 2
  1. 1.Mathematics Research CenterUniversity of WisconsinMadisonUSA
  2. 2.G.D. Searle & Co.SkokieUSA

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