Applied Asymptotics: Case Studies in Small-Sample Statistics

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Cambridge University Press, May 31, 2007 - Business & Economics - 236 pages
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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. Author resource page: http://www.isib.cnr.it/~brazzale/AA/
 

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Contents

Introduction
1
Uncertainty and approximation
5
23 Several parameters
10
24 Further remarks
14
Simple illustrations
17
33 Top quark
20
34 Astronomer data
23
35 Cost data
28
75 Vector parameter of interest
121
76 Laplace approximation
123
77 Partial likelihood
127
78 Constructed exponential families
129
Likelihood approximations
134
83 First order theory
138
84 Higher order density approximations
140
85 Tail area approximations
147

Discrete data
37
42 Urine data
39
43 Cell phone data
46
44 Multiple myeloma data
49
45 Speed limit data
52
46 Smoking data
55
Regression with continuous responses
58
52 Nuclear power station data
61
53 Daphnia magna data
66
54 Radioimmunoassay data
72
55 Leukaemia data
78
56 PET film data
81
Some case studies
86
63 Grazing data
91
64 Herbicide data
96
Further topics
108
73 Variance components
111
74 Dependent data
117
86 Tail area expressions for special cases
155
87 Approximations for Bayesian inference
161
88 Vector parameters of interest
164
Numerical implementation
170
92 Buildingblocks
171
93 Pivot profiling
174
94 Family objects and symbolic differentiation
177
95 Other software
182
Problems and further results
185
Some numerical techniques
211
A3 Laplace approximation
216
A4 X² approximations
217
References
219
Example index
229
Name index
230
Index
233
Copyright

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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.