Applied Asymptotics Case Studies in Small-Sample Statistics

About this book

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.

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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Biography

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 Federale de Lausanne. Nancy Reid is a University Professor of Statistics at the University of Toronto.