Applied Asymptotics: Case Studies in Small-Sample Statistics (Cambridge Series in Statistical and Probabilistic Mathematics)
Cambridge University Press, 5/31/2007
EAN 9780521847032, ISBN10: 0521847036
Hardcover, 248 pages, 26 x 18.5 x 1.8 cm
Language: English
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.
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.
'...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