Mathematical Methods of Statistics. (PMS-9)

Rating:
Summary: reprint of classic work
Review: Princeton University Press originally published this book in the mid 1940s. At the time, Harold Cramer was a leading statistician in Sweden. The field of mathematical statistics was just being formalized and there were no existing books with good mathematical treatment of inference methods. Kolmogorov was developing a rigorous measure theoretic basis for probability while Fisher and Neyman were developing different schools of thought on statistical inference.

Cramer put together the standard reference on mathematical statistics which is still valuable today. This is the type of book to be enjoyed by mathematical statisticians looking at it from a historical perspective. Recent advances require those who need a modern course to study other texts.

Rating:
Summary: not the best book ...
Review: This book is a very old edition. The print quality is not that good. The book is target to real mathematicians, interested in the abstract foundations of probability. I think this was an excellent book in the past, but currently I found a much better book : 'Real analysis and probability' by R.M. Dudley. Dudley 's book is more modern, for instance mentioning banach spaces as the framework for probability. Dudley 's book also provides more rigor and is even more self contained. Cramers book is definetely a 'nice to have' for historical reasons, but if you want an excellent complete explanation of the abstract probability theory, then you definitely must read Dudley ....

Rating:
Summary: A Statistical Toure de Force
Review: This was the first textbook on modern mathematical statistics, and is still one of the best. This work was one of the key elements which transformed probability theory and statistics into rigorous and powerful branches of mathematics.

It begins with an introduction to the theory of integration and measures, assuming no more than a working knowledge of calculus, and is one of the best introductory expositions of measure theory available.

The second part of the book is on statistical inference, and follows the three giants of modern statistics, Fisher, Neyman and Pearson. Cramér explains the difficult subjects of confidence regions and Neyman-Pearson hypothesis testing clearly and convincingly. The closing portion of the book discuss analysis of variance and linear regression methods; and is supplemented with real-world examples throughout, leaning heavily on the data provided by the Swedish census.

This book is a classic, not least for its combination of lucidity and rigor. In recognition of its merits, it has been re-issued in an affordable paperback edition. It belongs on the shelf of anyone interested in statistical methods.