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This modern treatment of mathematical statistics is concise, yet detailed enough to give readers a solid foundation in all aspects of the field. Treatment of each topic is thorough enough to make the coverage self-contained for a course in probability, and exceptional care has been taken to balance theory with applications. In addition to classical probability theory, such modern topics as order statistics and limiting distributions are discussed, along with applied examples from a wide variety of fields. Discussions include the core mathematical statistics topics of estimation, testing, and confidence intervals; ranking and selection procedures; decision theory; nonparametric statistics; regression and ANOVA; and robust statistical procedures. Computer-assisted data analysis is discussed at several points, reflecting the importance of statistical computation to the field. FORTRAN programs and BMDP routines are included, as well as the highly popular SAS routines. Also looks at the potential contribution of expert systems to statistics.
| Price | Condition | Delivery | Seller | Action |
| $178.95 | Digital |
| WonderClub |
Fred Ferd
reviewed Modern mathematical statistics on January 11, 2019 Modern mathematical statistics
If queried, the mathematician that does not work in statistics will most likely not feel that there is a need for a separate course in matrices applied to statistics. There is no doubt that statisticians need to know a great deal about matrices, so the question comes down to whether the traditional math courses in linear algebra are sufficient. In either case, it is still of benefit to have one source that statisticians can consult as a reference for problems with matrices and this book can serve as that source.
Mathematicians with little experience in statistics will have no difficulty in understanding the contents of the book, as nearly all of it is mathematical rather than statistical in nature. The first three chapters are:
*) A review of elementary matrix algebra.
*) Vector spaces.
*) Eigenvalues and eigenvectors.
With the exception of ten pages devoted to random vectors in chapter 1, there were few major items gleaned from statistics. They could serve as the first three chapters of any book on matrix operations. While the remaining chapters do contain more statistical concepts, the overwhelming majority of the material does not involve problems in statistics. There are a large number of problems at the end of the chapters and solutions are not provided.
The remaining chapters are:
*) Matrix factorizations and matrix norms.
*) Generalized inverses.
*) Systems of linear equations.
*) Partitioned matrices.
*) Special matrices and matrix products.
*) Matrix derivatives and related topics.
*) Some special topics related to quadratic forms.
The level of difficulty is within the reach of an advanced undergraduate, although it was written for graduate students in statistics. In my opinion, previous experience in statistics would be helpful, but not required for a reader to understand the material. If you are looking for a book on matrix operations, this one will serve your purpose, independent of whether your focus is on statistics.
Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon.
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