Applied Asymptotics: Case Studies in Small-Sample Statistics

ISBN-13: 9780521847032 / Angielski / Twarda / 2007 / 236 str.

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

Opis

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. Author resource page: http: //www.isib.cnr.it/ brazzale/AA/

Recenzje

'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

Spis treści

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.