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
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.
Reviews
'…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
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