Mathematical Statistics

1. Front Matter

   Pages i-xxiii

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2. Getting Started

   Pages 1-7

3. Structural Models for Data

   Pages 9-49

4. Least Squares Methods

   Pages 51-87

5. Combinatorial Probability

   Pages 89-113

6. Other Probability Models

   Pages 115-144

7. Discrete Random Variables I: The Hypergeometric Process

   Pages 145-173

8. Discrete Random Variables II: The Bernoulli Process

   Pages 175-208

9. Random Vectors and Random Samples

   Pages 209-243

10. Maximum Likelihood Estimates for Discrete Models

    Pages 245-273

11. Continuous Random Variables I: The Gamma and Beta Families

    Pages 275-308

12. Continuous Random Variables II: Expectations and the Normal Family

    Pages 309-339

13. Continuous Random Vectors

    Pages 341-373

14. Sampling Statistics for the Linear Model

    Pages 375-402

15. Representing Distributions

    Pages 403-436

16. Back Matter

    Pages 437-454

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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.

• Bernoulli process
• Likelihood
• Logistic Regression
• Probability theory
• Random variable
• mathematical statistics
• statistics

"The book is very easy and enjoyable to read ... it offers a refreshing point of view in an area which has been dominated by texts following almost exclusively by theoretical expositions."
Short Book Reviews, Vol. 20/2, August 2000

• Department of Statistics, Virginia Polytechnic Institute, Blacksburg, USA

  George R. Terrell

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