Mathematical Statistics: Basic Ideas and Selected Topics, Vol I

by Peter J. Bickel, Kjell A. Doksum

This classic, time-honored introduction to the theory and practice of statistics modeling and inference reflects the changing focus of contemporary Statistics. Coverage begins with the more general nonparametric point of view and then looks at parametric models as submodels of the nonparametric ones which can be described smoothly by Euclidean parameters. Although some computational issues are discussed, this is very much a book on theory. It relates theory to conceptual and technical issues encountered in practice, viewing theory as suggestive for practice, not prescriptive. It shows readers how assumptions which lead to neat theory may be unrealistic in practice. Statistical Models, Goals, and Performance Criteria. Methods of Estimation. Measures of Performance, Notions of Optimality, and Construction of Optimal Procedures in Simple Situations. Testing Statistical Basic Theory. Asymptotic Approximations. Multiparameter Estimation, Testing and Confidence Regions. A Review of Basic Probability Theory. More Advanced Topics in Analysis and Probability. Matrix Algebra. For anyone interested in mathematical statistics working in statistics, bio-statistics, economics, computer science, and mathematics.

Genres: Mathematics

556 pages, Hardcover

First published February 4, 1983

Reviews

[Данило Судин · Rating 5 out of 5]

Підручник зі статистики, який можна сміливо називати "Статистика 2.0". Виклад доволі жорсткий - з рясним і щедрим використанням математичного апарату, але доведення - улюблена річ для книжок по статистиці від математиків - зведена до мінімуму. З іншого боку, автори не "розжовують" базові поняття статистики і теорії імовірностей (як може здатися з першого розділу), а переходять до доволі прикладних і важливих питань.
Загалом, в цій книзі дуже коротко і доступно описано суть методу оцінки максимуму правдоподібності (maximum likelihood), оцінку гіпотез та довірчі інтервали пов’язано між собою (чого роблять не всі автори), а також продемонстровано проблему потужності критеріїв. Тобто книжка може дати багато цікавих деталей та дрібниць для тих, хто вже має базові знання та застосовував їх на практиці.

[Zhenyu · Rating 2 out of 5]

It's only worth reading if everything the author claim is proven. This book is a little out of date, which is okay. It's not quite organized or well-formatted, which is tolerable.

The major issue I have with it is not rigorously proving everything. The statistical tools introduced are lackluster, while the subjects it tries to tackle are too difficult. The authors need to put more effort to introduce more tools instead of more difficult problems. This is the point of a "textbook".

By reading some exercise problems, I have a feeling that the author is teaching the readers how to cut down an oak tree with a shaver blade, instead of giving the reader a chainsaw.

[Goo · Rating 4 out of 5]

Useful as a reference. Some theorems are not proved rigorously (since it would in some cases require more advanced measure theoretic probability theory).