Applied Asymptotics: Case Studies in Small-Sample Statistics

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Cambridge University Press, May 31, 2007 - Mathematics
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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.
 

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Contents

Section 1
5
Section 2
9
Section 3
17
Section 4
22
Section 5
31
Section 6
37
Section 7
52
Section 8
58
Section 11
94
Section 12
99
Section 13
105
Section 14
108
Section 15
129
Section 16
134
Section 17
143
Section 18
160

Section 9
83
Section 10
86
Section 19
170
Section 20
185

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Page 11 - Examples are presented to show how ambiguities may arise from attempts to define and apply analogues of sufficiency and ancillarity in the presence of nuisance parameters. It is necessary to tread with caution if one wishes to avoid inconsistencies or unexpected consequences inherent in principles which, on first acquaintance, appear unexceptionable.

About the author (2007)

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 Fédérale de Lausanne.

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