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Other titles in the Cambridge Series in Statistical and Probabilistic Mathematic series:
Cambridge Series in Statistical and Probabilistic Mathematic #23: Applied Asymptotics: Case Studies in Small-Sample Statisticsby A. R. Brazzale
Synopses & Reviews
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.
New likelihood-based methods now allow very accurate approximations in finite samples and this book illustrates with realistic examples and case studies how to use the new theory. The treatment is oriented towards practice and is accompanied by code in the R language, enabling practitioners to apply the methods with ease.
First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.
About the Author
Alessandra Brazzale is a Researcher in Statistics at the Institute of Biomedical Engineering, Italian National Research Council, Padova.Anthony Davison is a Professor of Statistics at the Ecole Polytechnique Fédérale de Lausanne.Nancy Reid is a University Professor of Statistics at the University of Toronto.
Table of Contents
Preface; 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; Bibliography; Index.
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