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Applied Asymptotics

Applied Asymptotics
Case Studies in Small-Sample Statistics


Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: May 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521847032

£ 69.99

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About the Authors
  • In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.

    • First practical treatment of small-sample asymptotics
    • Clearly illustrates the use and effect of new likelihood-based methods with realistic examples and case studies
    • Accompanied by code in the R language (available online), allowing practitioners to apply the methods to a wide range of situations
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    Reviews & endorsements

    '…I welcome this book and wish it well in achieving some inroads into practical use of a large area of theoretical developments.' Journal of Applied Statistics

    'This is a very welcome book, on a very important topic.' Andrew Robinson, University of Melbourne

    'This is an excellent book for applied statisticians. It presents application of higher order asymptotic theory in likelihood in many different contexts. … I highly recommend the book to researchers looking for ways to improve accuracy in statistical testing. The book is well written, the examples are clear and because all examples can be verified by the reader through the provided packages and code in R, the analyses can be explored in great detail.' Biometrics

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    Product details

    • Date Published: May 2007
    • format: Hardback
    • isbn: 9780521847032
    • length: 248 pages
    • dimensions: 260 x 185 x 18 mm
    • weight: 0.604kg
    • contains: 49 b/w illus. 47 tables 69 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Uncertainty and approximation
    3. Simple illustrations
    4. Discrete data
    5. Regression with continuous responses
    6. Some case studies
    7. Further topics
    8. Likelihood approximations
    9. Numerical implementation
    10. Problems and further results
    Appendices - some numerical techniques: Appendix 1. Convergence of sequences
    Appendix 2. The sample mean
    Appendix 3. Laplace approximation
    Appendix 4. X2 approximations

  • Resources for

    Applied Asymptotics

    A. R. Brazzale, A. C. Davison, N. Reid

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  • Authors

    A. R. Brazzale, Università degli Studi di Modena e Reggio Emilia
    Alessandra Brazzale is a Researcher in Statistics at the Institute of Biomedical Engineering, Italian National Research Council, Padova.

    A. C. Davison, École Polytechnique Fédérale de Lausanne
    Anthony Davison is a Professor of Statistics at the Ecole Polytechnique Fédérale de Lausanne.

    N. Reid, University of Toronto
    Nancy Reid is a University Professor of Statistics at the University of Toronto.

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