Customer Reviews

Functional Data Analysis (Springer Series in Statistics)

5 star:		(4)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This book deals with statistical analyis of multivariate data which may be treated preferably as curves. Examples of such situations include multivariate time series data which are observed at unequally spaced intervals, and two-way data in social sciences, and many high-dimensional data. Since this is the first attempt at a systematic account of this rapidly growing area, it wisely chooses to focus on descriptive and exploratory techniques developed by the authors and others. The readers are well-advised to have some background on smoothing spline which is employed as the key modeling framework.

For curious readers like me, it still leaves more to be desired. For example, the theory is better prepared by Grenander (1981)'s Abstract Inference, while the practice is preceded by the vast work on analysis of space-time field (4-D var) in climate research using EOF, similar to the principal components, but applied to the 2-d field data. I would also like to see more discussion of alternative modeling techniques such as wavelets and kernel smoothing methods.

I find this book a handy reference, so would recommend to others for the same purpose.

Bernie Silverman is a great writer. Once again along with Ramsay he has written a very accessible book on an interesting but difficult topic. Functional data are series of curves. These kinds of data are often treated under the topic of longitundal data analysis and of course they can also be put under the general category of mutlivariate analysis. Because the x axis often represents time you may also view the analysis of these data as falling in the category of multivariate time series.
Jon Ramsay is a professor of psychology who has contributed to the research in multivariate analysis and has a lot of experience with important applications of functional data analysis. He has had many major publications on this topic in leading statistical journals and has made advances in curve registration and in the development of principal differential analysis.

What is exploited in the functional data analysis approach is the treatment of families of such functions through basis functions (wavelets, Fourier series, orthogonal polynomials etc.). The canonical example is a group of adult males whose growth curves are under study. Each curve has a similar shape but each individual has some differences in the asymptote and other parameters of the curve. Defining these parameters, chosing the approximating functions and assessing the fit to the data are all part of art of functional data analysis.

Silverman is an expert in smoothing and kernal density techniques and you will see his expertise and research contribution exhibited in this text. The roughness penalty approach is one method covered in this book and in more detail in a Chapman and Hall monograph with Green.

Registration of curves is a particular technique that is unique to functional data analysis. Other techniques discussed in the book are generalizations or extensions of existing multivariate techniques such as principal components and canonical correlations.

Shape and smoothness of a curve can be described through derivatives and so differential operators play an important role in functional data analysis. It has a chapter devoted to it and another chapter on a technique called principal differential analysis.

The book concludes with a forward looking chapter on the future of functional data analysis and the challenges that remain ahead.

Also look at the fine review on amazon by dataguru who emphasizes the exploratory aspects of the approach presented in this text and the need to have some knowledge of spline functions.

The authors introduce the field of functional data analysis. In a nutshell, they use the techniques of functional analysis (the field of mathematics that deals with spaces of functions and operators) to extend the techniques of multivariate statistics to situations where the data are functional. Silverman and Ramsay present several very well motivated examples that clearly demonstrate the utility of their techniques.

The techniques presented in Functional Data Analysis are potentially very useful to people working in a variety of fields. Ecologist's building dynamical models, engineers trying to classify sensor readings, and statisticians trying to understand how traditional multivariate techniques generalize to functional data can all benefit from this book.

In addition to presenting interesting and usable ideas, the authors' presentation is clear and easily read. This is a very good book!

FDA is a very important new topic in statistics and Ramsay and Silverman provide an accessible introduction to the topic.

Functional data occur when the data are curves. For instance, we might monitor growth of children sampled at a fairly fine grid over several years. Or we might consider reports of experienced pain in many patients over a fairly long period of time. Even when the data *seem* discrete (and given measurement error and a finite sampling rate all data really *are* discrete) there may be substantial advantages to treat them as continuous.

Functional analysis extends the notion of linear space that is the foundation of statistics to the infinite dimensional case. In a infinite dimensional space, a matrix equation becomes an integral equation, and so on. They provide a useful introduction to the topic, enough that a non-specialist can get into it. The big difference between this treatment and older ones is that Ramsay and Silverman emphasize that the data generating process is assumed to be continuous. Many older treatments of similar data involve no curve regularization or smoothing. Basically they ignore the underlying continuity. Ramsay and Silverman show there are substantial benefits to paying attention to the continuity. For instance, if we want to estimate the derivative of a sampled curve it's logical to use first differences. They demonstrate, however, that fitting a smooth to the curve, e.g., a spline, and then finding the derivative of the smooth curve often does a much better job. (Why? Differencing amplifies noise.)

Anyway, they cover topics of linear models, principal components, canonical correlation, and principal differential analysis in function spaces. Their general feel is fairly exploratory. The one thing this book is short of is long examples, which can be found in their companion volume Applied Functional Data Analysis.

this is a great first book on introductory functional data analysis. the strength of the book lies in the fact that it introduces all concepts intuitively at first, without overwhelming the reader with any formalities. for the more mathematically minded reader, this a good introduction to the subject, which can be later complemented with more formal textbooks on functional analysis.

Functional data analysis is a topic of increasing interest in the statistics community, and is most commonly applied to time-series and/or spatial-series data. The main idea is to begin one's analysis of the data by constructing a smoothed or interpolated version, and then do many of the standard statistical things (such as finding principle components or doing regressions) in that smoothed function space.

The book explains the ideas and methods behind functional data analysis very clearly, with a minimum of math and notation and with a number of recurring, illustrative examples. For those interested in quickly getting oriented to the basic concepts and perhaps trying them out, I found that a few days with this book is a good place to start. The authors have also published a book with more detailed applications worked out called "Applied Functional Data Analysis".