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Statistical Inference (Chapman & Hall/CRC Monographs on Statistics & Applied Probability), by S.D. Silvey
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- Sales Rank: #1333058 in Books
- Published on: 1975-03-01
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .56" w x 5.98" l, .64 pounds
- Binding: Hardcover
- 192 pages
Review
..."by far the best book on its topic." -International Statistical Reveiw
Most helpful customer reviews
29 of 29 people found the following review helpful.
nice and concise
By Michael R. Chernick
As a statistics graduate student in the mid 1970s I took the three quarter graduate course sequence in mathematical statistics from Brad Efron and Charles Stein at Stanford. Efron taught the first two quarters and Stein the third. Our "official" texts for the course were Rao's "Linear Statistical Inference" and Ferguson's decision theoretic text. The books were useful reference sources but we also relied heavily on the instructors notes and Lehmann's "Testing Statistical Hypotheses".
However when I was preparing for my qualifying exam, I found this monograph by Silvey to be very helpful. It is concise and thus is great as a refresher for the important fundamental concepts that are all covered very well. I find it to be a great reference source when I need to refresh my memory on important points.
The book is only 190 pages but covers all the basics of mathematical statistics. Chapter 1 introduces the concepts of hypothesis testing and decision theory. Chapter 2 develops the theory of minimum variance unbiased estimation, covering concepts of sufficiency, completeness, efficiency, Fisher information, the Cramer-Rao inequality and its generalization and the Rao-Blackwell theorem. Chapter 3 covers the method of least squares and presents the Gauss-Markov theorem, weighted least squares and theoretical properties under assumptions of normally distributed errors. Chapter 4 presents maximum likelihood and its large sample properties. Chapter 5 covers confidence sets and 6 hypothesis testing. To emphasize the conciseness, Chapter 5 is 7 pages and Chapter 6 only 14 pages (including exercises). Sequential tests are covered in Chapter 8, non-parametric methods in Chapter 9, the Bayesian approach in Chapter 10 and basic decision theory in Chapter 11.
It is a shame that this book is out of print. An Amazon reader who is a statistics graduate student asked me for help understanding the Neyman-Pearson theory. Since he is having difficulty with his class text he was looking for a better source. Lehmann's book gives the rigorous mathematical proofs but I recommended Silvey as perhaps a better source for getting some insight. He may try to get a copy through Amazon. If so I hope that Amazon can find one for him!
0 of 0 people found the following review helpful.
Five Stars
By Noriko Gordon
It was great! Everything is perfect. Thank you!
7 of 7 people found the following review helpful.
Concise and Insightful
By H. D. Nguyen
This is an excellent text on statistics for serious, mathematically-minded readers. It covers every basic point in statistics in a concise and somewhat abstract manner without heavy use of measure theory. Personally, I am not very fond of abstractness, and this book does a good job of motivating the concepts. Therefore, the application-oriented reader will, hopefully, maintain his interest despite the reading being somewhat dense. It's a good reference and DEFINITELY not a bedtime read--unless, of course, you want to dream about those sexy math symbols.
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