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Full Description
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.
Contents
I Information and Likelihood.- I Recovery of Ancillary Information.- II Statistical Information and Likelihood Part I: Principles.- III Statistical Information and Likelihood Part II: Methods.- IV Statistical Information and Likelihood Part III: Paradoxes.- V Statistical Information and Likelihood: Discussions.- VI Partial Sufficiency.- VII Elimination of Nuisance Parameters.- VIII Sufficiency and Invariance.- IX Ancillary Statistics, Pivotal Quantities and Confidence.- II Survey Sampling and Randomization.- X Sufficiency in Survey Sampling.- XI Likelihood Principle and Survey Sampling.- XII On the Logical Foundations of Survey Sampling.- XIII On the Logical Foundations of Survey Sampling: Discussions.- XIV Relevance of Randomization in Data Analysis.- XV The Fisher Randomization Test.- XVI The Fisher Randomization Test: Discussions.- III Miscellaneous Notes and Discussions.- XVII Likelihood and Partial Likelihood.- XVIII A Discussion on the Fisher Exact Test.- XIX A Discussion on Survey Theory.- XX A Note on Unbiased Estimation.- XXI The Concept of Asymptotic Efficiency.- XXII Statistics Independent of a Complete Sufficient Statistic.- XXIII Statistics Independent of a Sufficient Statistic.- XXIV The Basu Theorems.- References.
