Applied Asymptotics: Case Studies in Small-Sample Statistics (Cambridge Series in Statistical and Probabilistic Mathematics)

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A. R. Brazzale, A. C. Davison, N. ReidCambridge University Press, 5/31/2007EAN 9780521847032, ISBN10: 0521847036Hardcover, 248 pages, 26 x 18.5 x 1.8 cmLanguage: EnglishIn fields s uch 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.Preface1. Introduction2. Uncertainty and approximation3. Simple illustrations4. Discrete data5. Regression with continuous responses6. Some case studies7. Further topics8. Likelihood approximations9. Numerical implementation10. Problems and further resultsAppendices - some numerical techniquesAppendix 1. Convergence of sequencesAppendix 2. The sample meanAppendix 3. Laplace approximationAppendix 4. X2 approximationsBibliographyIndex.'...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 Show more