Non-Standard Parametric Statistical Inference
Publisher: Oxford University Press
Published: September 15, 2017
Place of publication: Oxford, United Kingdom
Language: eng
Format: Hardcover
Number of pages: 432
ISBN-13: 9780198505044
Description: 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.
Notes: 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. 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. Includes bibliographical references (pages 393-406) and indexes.
Table of contents: title: -Introduction; title: -Non-standard problems: some examples --; title: -Standard asymptotic theory --; title: -Bootstrap analysis --; title: -Embedded model problem --; title: -Examples of embedded distributions --; title: -Embedded distributions: two numerical examples --; title: -Infinite likelihood --; title: -The Pearson and Johnson systems --; title: -Box-Cox transformations --; title: -Change-point models --; title: -The skew normal distribution --; title: -Randomized-parameter models --; title: -Indeterminacy --; title: -Nested nonlinear regression models --; title: -Bootstrapping linear models --; title: -Finite mixture models --; title: -Finite mixture examples, MAPIS details.