Nonparametric Functional Data Analysis: Theory And Practice

This is a research monograph rather than a practical book or, even less, a textbook. For the latter, your needs are better served by Ramsay and Silverman (2005a, b). In a sense, the present book is heavily biased toward statistical theory and is weak on practice and applications. For the theory aspect, the present book does bring something new and, indeed, some novel theoretical investigations into the kinds of functional data problems not addressed by Ramsay and Silverman (2005a). While Ramsay and Silverman’s books focus on exploratory and data analytic techniques for sparsely observed functional data, and employ techniques for smoothing and extrapolation using smoothing spline methods, the present book focuses on issues that arise from analysis of high resolution functional data, which can be easily registered or made to balance (pp. 33–34). The present book applies kernel regression techniques to functional data problems such as functional regression or classification, where the predictor is a function. The use of “nonparametric” in the title, although appropriate, is not totally distinctive, because I consider most techniques used in Ramsay and Silverman (2005a) nonparametric as well. The book mentions several applications in chemometrics, speech recognition, and electricity consumption forecast. I would like to add more, such as climate data analysis, material sciences, and bioinformatics. As someone who works closely with scientists on various interdisciplinary investigations on a daily basis, I feel strongly that there is need for new statistics that can deal with increasingly high throughput and high resolution measurements. Modern data analysis can benefit greatly from the recent statistical advent in functional data analysis. I think there will be many developments in the area of high-dimensional statistics when there are more observed variables than the number of replicates or samples, and multivariate statistics should receive revived interest in statistical research. In a sense, rather than sticking strictly with the existing techniques, one should adopt a pioneering attitude toward functional data analysis, and professional statisticians should be prepared to develop on their own techniques appropriate for a given problem, because much new statistics remains to be developed for the emerging problems (Lu 2006). Nonparametric statisticians should feel very much at home with the approach taken in this book. The authors have defined a broad and interesting framework in Part I, such as functional statistics, semimetrics, and locally weighted regression for functional data. Theoretical results, mainly asymptotics, are provided in Part II. Part V also contains some relevant theory and should be read right after Part II. I should point out some very relevant early work on nonparametric regression with fractal design (Lu 1999). Part III of the book deals with classification problems of functional data. Part IV is unusual, in that it deals with time series and dependent data. Although time series is among my favorite subject, it does not appear obvious how this part fits into the functional data framework, although one may argue that for high frequency time series, functional statistics may be very relevant. Notwithstanding, I do think the present book is a worthy contribution to the literature. The authors have done a nice job of summarizing some of ongoing research, on which some of the papers exist only in proceedings or in the French literature. Researchers in the growing functional statistics community should be glad to have a copy of the book.