Non-Standard Parametric Statistical Inference

ISBN : 9780198505044

Russell C. H. Cheng
432 Pages
156 x 234 mm
Pub date
Jun 2017
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This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on: (i) how to recognize situations where the problem is non-standard when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analyzing such problems. A frequentist likelihood-based viewpoint is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically, with only sufficient mathematical detail to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods, as is typically covered in a university statistical inference course, wishing to understand or study how standard methodology might fail. Easy to understand statistical methods are presented which overcome these difficulties, and demonstrated by detailed examples drawn from real applications. Simple and practical model-building is an underlying theme. Parametric bootstrap resampling is used throughout for analyzing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing an accessible demonstration of the sampling behaviour of estimators.


1 Introduction
2 Non-Standard Problems: Some Examples
3 Standard Asymptotic Theory
4 Bootstrap Analysis
5 Embedded Model Problem
6 Examples of Embedded Distributions
7 Embedded Distributions: Two Numerical Examples
8 Infinite Likelihood
9 The Peason and Johnson Systems
10 Box-Cox Transformations
11 Change-Point Models
12 The Skew Normal Distribution
13 Randomized-Parameter Models
14 Indeterminacy
15 Nosted Nonlinear Regression Models
16 Bootstrapping Linear Models
17 Finite Mixture Models
18 Finite Mixture Examples: Mapis Details

About the author: 

Russell Cheng is Emeritus Professor of Operational Research at the University of Southampton. He has an M.A. and a Diploma in Mathematical Statistics from Cambridge University, and obtained his Ph.D. from Bath University. He is a former Chairman of the U.K. Simulation Society, a former Fellow of the Royal Statistical Society, and Fellow of the Institute of Mathematics and Its Applications. His research interests include: design and analysis of simulation experiments and parametric estimation methods. He founded and was Joint Editor of the IMA Journal of Management Mathematics.

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