Mathematical Statistics (Chapman & Hall/CRC Texts in Statistical Science) [Hardcover]

Keith Knight (Author)

Book Description

ISBN-10: 158488178X | ISBN-13: 978-1584881780 | Publication Date: November 24, 1999 | Edition: 1

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

Product Details

• Hardcover: 504 pages
• Publisher: Chapman and Hall/CRC; 1 edition (November 24, 1999)
• Language: English
• ISBN-10: 158488178X
• ISBN-13: 978-1584881780
• Product Dimensions: 9.7 x 6.1 x 1.3 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 2.7 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #2,111,446 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

37 of 37 people found the following review helpful:

4.0 out of 5 stars modern math stat, February 25, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Mathematical Statistics (Chapman & Hall/CRC Texts in Statistical Science) (Hardcover)

With so many good graduate texts available to choose from I think it is more helpful for me to tell you what this offers that some of the others do not and then you can decide for yourself if it is for you. It is not the best written text and is highly mathematical. It does introduce some modern concepts such as empirical likelihood,the jackknife, and the bootstrap and devotes a chapter to the important topic of generalized linear models. However, the bootstrap is only mentioned briefly as a resampling tool that can be used in the context of generalized linear models. Its more general use as a competitor to the jackknife for estimation of variance or standard errors and in the context of confidence intervals is not mentioned.

An avantage of the book for some is that it includes chapters on probability theory. It only includes the topics needed to understand distribution theory for inference purposes and to be able to understand asymptotic distributions. To achieve this Knight covers the basic rules of probability and its measrue theoretic basis in chapter one. Inportant convergence results needed to develop the asymptotic theory of statistics is cover in Chapter 3 where the concepts of convergence in probability and convergence in distribution are given along with key results such as the weak law of large numbers and the central limot theorem. This is a nice feature as it makes the book self-contained and the student does not need a book or separate course in advanced probability since the essence of that material is covered in Chapters 1 and 3.

I do applaud the author for covering important topics such as generalized linear models along with the standard parametric theory of hypothesis testing and estimation. Another topic not commonly covered in the affect of model mispecification on results.

So if you are interested in learning about the jackknife, empirical likelihood and the Bayesian approach, this is one of very few advanced books that covers all these topics and still covers probability and standard statidtical theory (e.g. Cramer-Rao inequality, Lehmann-Scheffe theorem, Neyman Pearson lemma, uniformly most powerful tests, Basu's lemma, and sufficiency and efficiency concepts.

6 of 6 people found the following review helpful:

2.0 out of 5 stars Advanced Text - Poor Reference Tool, Many Typos, December 4, 2003

By 

Derek W. Hoiem (Pittsburgh, PA United States) - See all my reviews
(REAL NAME)   

This review is from: Mathematical Statistics (Chapman & Hall/CRC Texts in Statistical Science) (Hardcover)

I used this book in a class that I took for intermediate statistics, a mid-level graduate course in the statistics department at a top university. This is an advanced book on mathematical statistics. In general, I found that if I had significant exposure to a topic previously, I could easily understand the text. Sections of the book containing topics new to me, however, were difficult to understand. The biggest failure of this book to me is that it serves as a poor reference tool. Definitions, theorems, and important concepts are often hidden in paragraphs nestled between examples. There is no appendix or list of distributions, moment generating functions, etc. The index is incomplete. A second negative aspect of the book is that there are many typos. The extent of the typos often increases the difficulty of understanding the text.

Overall, this book should never be used for an undergraduate course. I also do not recommend this book for use in a graduate course, unless some later edition with heavy revisions is released. I strongly recommend not buying this book for personal use as a reference tool.

2 of 2 people found the following review helpful:

4.0 out of 5 stars 3 and a half stars actually, June 29, 2005

By 

ReBorn (Toronto) - See all my reviews

This review is from: Mathematical Statistics (Chapman & Hall/CRC Texts in Statistical Science) (Hardcover)

This book is very challenging for a beginner student in statistics. I am not sure how it would be if one had some preparation in the subject, but I still think that it should rather be used as a source for excercises and some concepts. However, using it can be a little frustrating sometimes. Let me give you an example: If you want to do some exercise which requires you to know a density function of a certain random variable then you have to look somewhere else because this book fails to provide you with a table of most common distributions. Also there are a lot of typos. Some exercises overcomplicate things, e.g. they are not about understanding a concept but giving you hard calculations to do. OK, as far as positive things about it: Some examples are good, definitions are precise, and most of exercises will make you think. Overall, I would recommend it only if you have mastered the basics. It would probably be useful with an excellent teacher who would explain the concepts to make you look at the material from a different point of view.