Ebook: Statistical Information and Likelihood: A Collection of Critical Essays by Dr. D. Basu

It is an honor to be asked to write a foreword to this book, for I believe that it and other books to follow will eventually lead to a dramatic change in the current statistics curriculum in our universities. I spent the 1975-76 academic year at Florida State University in Tallahassee. My purpose was to complete a book on Statistical Reliability Theory with Frank Proschan. At the time, I was working on total time on test processes. At the same time, I started attending lectures by Dev Basu on statistical inference. It was Lehmann's hypothesis testing course and Lehmann's book was the text. However, I noticed something strange - Basu never opened the book. He was obviously not following it. Instead, he was giving a very elegant, measure theoretic treatment of the concepts of sufficiency, ancillarity, and invariance. He was interested in the concept of information - what it meant. - how it fitted in with contemporary statistics. As he looked at the fundamental ideas, the logic behind their use seemed to evaporate. I was shocked. I didn't like priors. I didn't like Bayesian statistics. But after the smoke had cleared, that was all that was left. Basu loves counterexamples. He is like an art critic in the field of statistical inference. He would find a counterexample to the Bayesian approach if he could. So far, he has failed in this respect.

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This book is a collection of essays on the foundations of Statistical Inference. The sequence in which the essays have been arranged makes it possible to read the book as a single contemporay discourse on the likelihood principle, the paradoxes that attend its violation, and the radical deviation from classical statistical practices that its adoption would entail. The book can also be read, with the aid of the notes as a chronicle of the development of Basu's ideas.

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This book is a collection of essays on the foundations of Statistical Inference. The sequence in which the essays have been arranged makes it possible to read the book as a single contemporay discourse on the likelihood principle, the paradoxes that attend its violation, and the radical deviation from classical statistical practices that its adoption would entail. The book can also be read, with the aid of the notes as a chronicle of the development of Basu's ideas.
Content:
Front Matter....Pages N2-xviii
Front Matter....Pages xix-xix
Recovery of Ancillary Information....Pages 1-19
Statistical Information and Likelihood....Pages 20-42
Statistical Information and Likelihood....Pages 43-59
Statistical Information and Likelihood....Pages 60-77
Statistical Information and Likelihood Discussions....Pages 78-97
Partial Sufficiency....Pages 98-113
Elimination of Nuisance Parameters....Pages 114-141
Sufficiency and Invariance....Pages 142-160
Ancillary Statistics, Pivotal Quantities and Confidence Statements....Pages 161-176
Front Matter....Pages N3-N3
Sufficiency in Survey Sampling....Pages 177-185
Likelihood Principle and Survey Sampling....Pages 186-200
On the Logical Foundations of Survey Sampling....Pages 201-233
On the Logical Foundations of Survey Sampling Discussions....Pages 234-244
Relevance of Randomization in Data Analysis....Pages 245-270
The Fisher Randomization Test....Pages 271-289
The Fisher Randomization Test: Discussions....Pages 290-312
Front Matter....Pages N4-N4
Likelihood and Partial Likelihood....Pages 313-320
A Discussion on the Fisher Exact Test....Pages 321-324
A Discussion on Survey Theory....Pages 325-328
A Note on Unbiased Estimation....Pages 329-332
Front Matter....Pages N4-N4
The Concept of Asymptotic Efficiency....Pages 333-336
Statistics Independent of a Complete Sufficient Statistic....Pages 337-341
Statistics Independent of a Sufficient Statistic....Pages 342-344
The Basu Theorems....Pages 345-349
Back Matter....Pages 350-369

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This book is a collection of essays on the foundations of Statistical Inference. The sequence in which the essays have been arranged makes it possible to read the book as a single contemporay discourse on the likelihood principle, the paradoxes that attend its violation, and the radical deviation from classical statistical practices that its adoption would entail. The book can also be read, with the aid of the notes as a chronicle of the development of Basu's ideas.
Content:
Front Matter....Pages N2-xviii
Front Matter....Pages xix-xix
Recovery of Ancillary Information....Pages 1-19
Statistical Information and Likelihood....Pages 20-42
Statistical Information and Likelihood....Pages 43-59
Statistical Information and Likelihood....Pages 60-77
Statistical Information and Likelihood Discussions....Pages 78-97
Partial Sufficiency....Pages 98-113
Elimination of Nuisance Parameters....Pages 114-141
Sufficiency and Invariance....Pages 142-160
Ancillary Statistics, Pivotal Quantities and Confidence Statements....Pages 161-176
Front Matter....Pages N3-N3
Sufficiency in Survey Sampling....Pages 177-185
Likelihood Principle and Survey Sampling....Pages 186-200
On the Logical Foundations of Survey Sampling....Pages 201-233
On the Logical Foundations of Survey Sampling Discussions....Pages 234-244
Relevance of Randomization in Data Analysis....Pages 245-270
The Fisher Randomization Test....Pages 271-289
The Fisher Randomization Test: Discussions....Pages 290-312
Front Matter....Pages N4-N4
Likelihood and Partial Likelihood....Pages 313-320
A Discussion on the Fisher Exact Test....Pages 321-324
A Discussion on Survey Theory....Pages 325-328
A Note on Unbiased Estimation....Pages 329-332
Front Matter....Pages N4-N4
The Concept of Asymptotic Efficiency....Pages 333-336
Statistics Independent of a Complete Sufficient Statistic....Pages 337-341
Statistics Independent of a Sufficient Statistic....Pages 342-344
The Basu Theorems....Pages 345-349
Back Matter....Pages 350-369
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