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Statistical Inference
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Probability and Statistical Inference, Second Edition is a user-friendly book that stresses the comprehension of concepts instead of the simple acquisition of a skill or tool. It provides a mathematical framework that permits students to carry out various procedures using any number of computer software packages as opposed to relying on one particular package. Its unique approach to problems allows readers to integrate the knowledge gained from the text... enhancing a more complete and honest understanding of the topic.
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In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies.
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Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time. It includes:
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Statistical inference for a system of simultaneous, nonlinear, implicit equations is discussed. The discussion considers inference as an adjunct to maximum likelihood estimation rather than in a general setting. The null and non-null asymptotic distributions of the Wald test, the Lagrange multiplier test (Rao's efficient score test), and the likelihood ratio test are obtained. Several refinements in the existing theory of maximum likelihood estimation are accomplished as intermediate steps.
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This paper addresses the problem that Bayesian statistical inference cannot accommodate theory change, and proposes a framework for dealing with such changes. It first presents a scheme for generating predictions from observations by means of hypotheses. An example shows how the hypotheses represent the theoretical structure underlying the scheme. This is followed by an example of a change of hypotheses. The paper then presents a general framework for hypotheses change, and proposes the minimization of the distance between hypotheses as a rationality criterion. Finally the paper discusses the import of this for Bayesian statistical inference.
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Adopting a broad view of statistical inference, this text concentrates on what various techniques do, with mathematical proofs kept to a minimum. The approach is rigorous, but will be accessible to final year undergraduates. Classical approaches to point estimation, hypothesis testing and interval estimation are all covered thoroughly, with recent developments outlined. Separate chapters are devoted to Bayesian inference, to decision theory and to non-parametric and robust inference. The increasingly important topics of computationally intensive methods and generalized linear models are ... included. In this edition, the material on recent developments has been updated, and additional exercises are included in most chapters.
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Statistical Inference