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Applied Asymptotics Case Studies in Small Sample Statistics 1st Edition by AR Brazzale, AC Davison, N Reid ISBN 0521847036 9780521847032

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Applied Asymptotics Case Studies in Small Sample Statistics 1st Edition Brazzale A. R. Digital Instant Download

Author(s): Brazzale A. R., Reid N., Davison A. C.
ISBN(s): 9780521847032, 0521847036
Edition: 1
File Details: PDF, 3.32 MB
Year: 2007
Language: english
SKU: EB-973702 Category: Tags: , ,

Applied Asymptotics Case Studies in Small Sample Statistics 1st Edition by AR Brazzale, AC Davison, N Reid – Ebook PDF Instant Download/Delivery: 0521847036, 9780521847032
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ISBN 10: 0521847036 
ISBN 13: 9780521847032
Author: AR Brazzale, AC Davison, N Reid

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.

Applied Asymptotics Case Studies in Small Sample Statistics 1st Table of contents:

1. Introduction

  • Bibliographic notes

2. Uncertainty and Approximation

2.1 Introduction
2.2 Scalar parameter
2.3 Several parameters
2.4 Further remarks

  • Bibliographic notes

3. Simple Illustrations

3.1 Introduction
3.2 Cauchy distribution
3.3 Top quark
3.4 Astronomer data
3.5 Cost data

  • Bibliographic notes

4. Discrete Data

4.1 Introduction
4.2 Urine data
4.3 Cell phone data
4.4 Multiple myeloma data
4.5 Speed limit data
4.6 Smoking data

  • Bibliographic notes

5. Regression with Continuous Responses

5.1 Introduction
5.2 Nuclear power station data
5.3 Daphnia magna data
5.4 Radioimmunoassay data
5.5 Leukaemia data
5.6 PET film data

  • Bibliographic notes

6. Some Case Studies

6.1 Introduction
6.2 Wasp data
6.3 Grazing data
6.4 Herbicide data

  • Bibliographic notes

7. Further Topics

7.1 Introduction
7.2 Calibration
7.3 Variance components
7.4 Dependent data
7.5 Vector parameter of interest
7.6 Laplace approximation
7.7 Partial likelihood
7.8 Constructed exponential families

  • Bibliographic notes

8. Likelihood Approximations

8.1 Introduction
8.2 Likelihood and model classes

8.3 First Order Theory
8.3.1 Scalar Θ
8.3.2 Vector Θ

8.4 Higher Order Density Approximations
8.4.1 The p approximation
8.4.2 The tangent exponential model
8.4.3 Ancillary directions

8.5 Tail Area Approximations
8.5.1 Introduction
8.5.2 No nuisance parameters
8.5.3 Nuisance parameters
8.5.4 Discrete random variables

8.6 Tail Area Expressions for Special Cases
8.6.1 Linear exponential family
8.6.2 Non-normal linear regression
8.6.3 Nonlinear regression

8.7 Approximations for Bayesian inference

8.8 Vector Parameters of Interest
8.8.1 Introduction
8.8.2 Bartlett correction
8.8.3 Skovgaard’s approximation

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Tags: AR Brazzale, AC Davison, N Reid, Asymptotics