Customer Reviews

Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley Series in Probability and Statistics)

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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.

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.

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