Mathematical Statistics - George R. Terrell

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Résumé :
Whyanothertextbook? The statistical community generally agrees that at the upper undergraduate level, or the beginning master?s level, students of statistics should begin to study the mathematical methods of the ?eld. We assume that by thentheywillhavestudiedtheusualtwo yearcollegesequence,includingcalculus through multiple integrals and the basics of matrix algebra. Therefore, they are ready to learn the foundations of their subject, in much more depth than is usual in an applied, ?cookbook,? introduction to statistical methodology. There are a number of well written, widely used textbooks for such a course. These seem to re?ect a consensus for what needs to be taught and how it should be taught. So, why do we need yet another book for this spot in the curriculum? I learned mathematical statistics with the help of the standard texts. Since then, Ihavetaughtthiscourseandsimilaronesmanytimes,atseveraldifferentuniversi ties,usingwell thought oftextbooks.Butfromthebeginning,Ifeltthatsomething was wrong. It took me several years to articulate the problem, and many more to assemble my solution into the book you have in your hand. You see, I spend the rest of my day in statistical consulting and statistical re search. I should have been preparing my mathematical statistics students to join me in this exciting work. But from seeing what the better graduating seniors and beginning graduate students usually knew, I concluded that the standard curricu lumwasnotteachingthemtobesophisticatedcitizensofthestatisticalcommunity.

Sommaire:
Getting Started.- Structural Models for Data.- Least Squares Methods.- Combinatorial Probability.- Other Probability Models.- Discrete Random Variables I: The Hypergeometric Process.- Discrete Random Variables II: The Bernoulli Process.- Random Vectors and Random Samples.- Maximum Likelihood Estimates for Discrete Models.- Continuous Random Variables I: The Gamma and Beta Families.- Continuous Random Variables II: Expectations and the Normal Family.- Continuous Random Vectors.- Sampling Statistics for the Linear Model.- Representing Distributions.