Mathematical Statistics: A Unified Introduction (Springer Texts in Statistics) - Hardcover

Terrell, George R.

Hardcover

ISBN 10: 0387986219 ISBN 13: 9780387986210

Publisher: Springer, 1999

Synopsis

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.

About this title

Review

"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

Synopsis

This textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed; this is developed as needed. The book is committed to a high level of mathematical seriousness; and to an intimate connection with application. Modern methods, such as logistic regression, are introduced; as are unjustly neglected clasical topics, such as elementary asymptotics. The book first develops elementary linear models for measured data and multiplicative models for counted data. Simple probability models for random error follow. The most important famiies of random variables are then studied in detail, emphasizing their interrelationships and their large-sample behavior. Inference, including classical, Bayesian, finite population, and likelihood-based, is introduced as the necessary mathematical tools become available.

In teaching style, the book aims to be * mathematically complete: every formula is derived, every theorem proved at the appropriate level * concrete: each new concept is introduced and exemplified by interesting statistical problems; and more abstract concepts appear only gradually * constructive: direct derivations and proofs are preferred * active: students are led to do mathematical statistics, not just to appreciate it, with the assistance of 500 interesting exercises. The text is aimed for the upper undergraduate level, or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite series. George R. Terrell received his degrees from Rice University, where he later taught. Since 1986 he has taught in the Statistics Department of

Edition details

• Publisher: Springer
• Publication date: 1999
• Language: English
• ISBN 10: 0387986219
• ISBN 13: 9780387986210
• Binding: Hardcover
• Number of pages: 472