Skip to main content
SpringerLink
Log in
Book cover

Applied Statistical Inference pp 79–122Cite as

Frequentist Properties of the Likelihood

  • Chapter

Abstract

Frequentist properties of the maximum likelihood estimate of a scalar parameter are derived. The Wald, Score and Likelihood Ratio test statistics and the corresponding confidence intervals are introduced. Variance stabilizing transformations are also discussed. A case study comparing coverage and width of several confidence intervals for a proportion finishes this chapter, completed by a number of exercises at the end.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bayarri, M. J., & Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statistical Science, 19(1), 58–80.

    Article  MathSciNet  MATH  Google Scholar 

  • Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133.

    MathSciNet  MATH  Google Scholar 

  • Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4), 404–413.

    Article  MATH  Google Scholar 

  • Connor, J. T., & Imrey, P. B. (2005). Proportions, inferences, and comparisons. In P. Armitage & T. Colton (Eds.), Encyclopedia of biostatistics (2nd ed., pp. 4281–4294). Chichester: Wiley.

    Google Scholar 

  • Davison, A. C. (2003). Statistical models. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Lehmann, E. L., & Casella, G. (1998). Theory of point estimation (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Millar, R. B. (2011). Maximum likelihood estimation and inference: with examples in R, SAS and ADMB. New York: Wiley.

    Book  Google Scholar 

  • Newcombe, R. G. (2013). Chapman & Hall/CRC biostatistics series. Confidence intervals for proportions and related measures of effect size. Boca Raton: CRC Press. ISBN 978-1-4398-1278-5.

    Google Scholar 

  • Pawitan, Y. (2001). In all likelihood: statistical modelling and inference using likelihood. New York: Oxford University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Social and Preventive Medicine, University of Zurich, Zurich, Switzerland

    Leonhard Held & Daniel Sabanés Bové

Authors
  1. Leonhard Held
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Sabanés Bové
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Held, L., Sabanés Bové, D. (2014). Frequentist Properties of the Likelihood. In: Applied Statistical Inference. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37887-4_4

Download citation

Publish with us

Policies and ethics

Search

Navigation