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Introduction to Statistical Theory
Introduction to Statistical Theory
- GenresMathematics
237 pages, Hardcover
First published January 1, 1971
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January 18, 2021
This book is the second installment of a three-volume set beginning with Introduction to Probability Theory. While there are many other statistics books, this volume is ideal for those who used the previous book to learn the basics of probability. The terminology, notation, and so forth are identical. The book covers the basic theoretical underpinnings of statistics (loss functions, unbiased estimates, maximum likelihood, etc.), hypothesis tests, linear models, and non-parametric methods. Where relevant, the book demonstrates the use of Bayesian methods. The vast majority of the techniques described are accompanied by proofs that justify their validity.
While mathematical truths are eternal, applied problem-solving techniques are not, and it will be obvious to the reader that the book is from a time when computers were rare. The book demonstrates several approaches (such as normal approximations to binomial distributions or the subtraction of constants from data sets when doing autocorrelation tests) that are no longer necessary. Printed tables of random numbers and square roots, both of which are included in the back of the book, are anachronistic. And one exercise even bears the charming warning that the student should not "work this problem unless a calculating machine is available." All that said, though, the text and the exercises are still valuable.
The exercises provided are valuable, particularly as numerical answers (not full solutions showing steps) to many of the problems are provided in the book. Unfortunately, the solutions are marred by the occasional error. When one encounters a solution that does not match one's own, one must therefore not automatically assume an error on one's own part. (However, it seems appropriate to note, given that the book is about statistics, that when such a discrepancy arises, the most likely reason is a mistake on the reader's part -- absent Bayesian priors about the reader's abilities.)
While I am confident that most readers would do better with a more modern book, I found the book served my purposes well. It was, as expected, an excellent statistical complement to the previous probability book.
While mathematical truths are eternal, applied problem-solving techniques are not, and it will be obvious to the reader that the book is from a time when computers were rare. The book demonstrates several approaches (such as normal approximations to binomial distributions or the subtraction of constants from data sets when doing autocorrelation tests) that are no longer necessary. Printed tables of random numbers and square roots, both of which are included in the back of the book, are anachronistic. And one exercise even bears the charming warning that the student should not "work this problem unless a calculating machine is available." All that said, though, the text and the exercises are still valuable.
The exercises provided are valuable, particularly as numerical answers (not full solutions showing steps) to many of the problems are provided in the book. Unfortunately, the solutions are marred by the occasional error. When one encounters a solution that does not match one's own, one must therefore not automatically assume an error on one's own part. (However, it seems appropriate to note, given that the book is about statistics, that when such a discrepancy arises, the most likely reason is a mistake on the reader's part -- absent Bayesian priors about the reader's abilities.)
While I am confident that most readers would do better with a more modern book, I found the book served my purposes well. It was, as expected, an excellent statistical complement to the previous probability book.
Displaying 1 of 1 review