Non-Standard Parametric Statistical Inference

This book will be of interest for practitioners, and might be used as an advanced undergraduate or introductory graduate textbook for a course in applied statistics and/or econometrics.

Autorentext

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.

Klappentext

This research monograph gives a unified view of non-standard estimation problems. It provides an overall mathematical framework, but also draws together and studies in detail a large number of practical problems, previously only treated separately, offering solution methods and numerical procedures for each.

Zusammenfassung
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.

Inhalt

• 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 Pearson and Johnson Systems
• 10: Box-Cox Transformations
• 11: Change-Point Models
• 12: The Skew Normal Distribution
• 13: Randomized-Parameter Models
• 14: Indeterminacy
• 15: Nested Nonlinear Regression Models
• 16: Bootstrapping Linear Models
• 17: Finite Mixture Models
• 18: Finite Mixture Examples: MAPIS Details