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Written to convey an intuitive feel for both theory and practice, its main objective is to illustrate what a powerful tool density estimation can be when used not only with univariate and bivariate data but also in the higher dimensions of trivariate and quadrivariate information. Major concepts are presented in the context of a histogram in order to simplify the treatment of advanced estimators. Features 12 four-color plates, numerous graphic illustrations as well as a multitude of problems and solutions.
- Sales Rank: #1939558 in Books
- Published on: 1992-08
- Original language: English
- Number of items: 1
- Dimensions: 9.41" h x .82" w x 6.34" l, 1.31 pounds
- Binding: Hardcover
- 317 pages
From the Publisher
Written to convey an intuitive feel for both theory and practice, its main objective is to illustrate what a powerful tool density estimation can be when used not only with univariate and bivariate data but also in the higher dimensions of trivariate and quadrivariate information. Major concepts are presented in the context of a histogram in order to simplify the treatment of advanced estimators. Features 12 four-color plates, numerous graphic illustrations as well as a multitude of problems and solutions.
From the Back Cover
Density estimation has long been recognized as an important tool when used with univariate and bivariate data. But the computer revolution of recent years has provided access to data of unprecedented complexity in ever-growing volume. New tools are required to detect and summarize the multivariate structure of these difficult data. Multivariate Density Estimation: Theory, Practice, and Visualization demonstrates that density estimation retains its explicative power even when applied to trivariate and quadrivariate data. By presenting the major ideas in the context of the classical histogram, the text simplifies the understanding of advanced estimators and develops links between the intuitive histogram and other methods that are more statistically efficient. The theoretical results covered are those particularly relevant to application and understanding. The focus is on methodology, new ideas, and practical advice. A hierarchical approach draws attention to the similarities among different estimators. Also, detailed discussions of nonparametric dimension reduction, nonparametric regression, additive modeling, and classification are included. Because visualization is a key element in effective multivariate nonparametric analysis, more than 100 graphic illustrations supplement the numerous problems and examples presented in the text. In addition, sixteen four-color plates help to convey an intuitive feel for both the theory and practice of density estimation in several dimensions. Ideal as an introductory textbook, Multivariate Density Estimation is also an indispensable professional reference for statisticians, biostatisticians, electrical engineers, econometricians, and other scientistsinvolved in data analysis.
Most helpful customer reviews
35 of 35 people found the following review helpful.
about the only practical book on the topic
By Michael R. Chernick
There are a number of good books dealing with univariate density estimates. Some are very theoretical and some are very practical. My favorite is the one by Silverman because it provides intuition for the kernel density estimation methods and gets to the key point. David Scott has produced a volume that is somewhat longer than Silverman's and is the only book I have found for estimating multivariate densities. He writes very clearly on a difficult topic and provides good graphical information.
14 of 14 people found the following review helpful.
Excellent treatment of the histogram
By A Customer
This self-contained title represents a thorough treatment of both univariate and multivariate density estimation, with an emphasis on multivariate applications not found in other texts. A valuable, and perhaps unique, feature of this book is its clear discussion of the theory of kernel density estimation in terms of the conventional histogram, the latter being quite intuitive to most students.
The author uses applied mathematics, expected value operations, and asymptotic theory to draw general conclusions about the relative performance between different density estimation techniques. The purpose is to provide estimators that are "optimal" for higher dimensioned problems, since the computational burden grows exponentially with higher dimensions (thus making exploratory data analysis more expensive). With this in mind, the author is justified to show how the thorough treatment of theory relates to practice and visualization.
Ideas are reinforced by many problems at the end of each chapter (I regret that the answers to these problems are not included, or would have otherwise preferred just a few more examples). One nice feature is the author puts boxes around the most important theorems and results, making them easier to identify for reference purposes later. There is an emphasis on the way univariate concepts extend to lower dimensional multivariate problems, so that only a minority of the text might be considered exclusively multivariate in scope. The book contains a valuable list of references and a terse but useful appendix on 3-D computer visualization.
As a result, this text educates on more than density estimation, but does so assuming a fairly sophisticated level of audience education and background beyond the first few chapters. Since most of the terminology and basic concepts are defined early on, yet the most interesting applications and methods are discussed toward the end, this title is not easily skimmed. I have found this book cited often by other texts in this fields.
4 of 5 people found the following review helpful.
essential
By Jan Galkowski
This has become of four texts I am constantly consulting.
The others?
Rice, MATHEMATICAL STATISTICS AND DATA ANALYSIS, 3rd edition.
Bivand, Pebesma, Gomez-Rubio, APPLIED SPATIAL DATA ANALYSIS WITH R
Ramsey, Schafer, THE STATISTICAL SLEUTH: A COURSE IN METHODS OF DATA ANLYSIS
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