Contents
Part I.Regression modeling for FDA:A unifying classification for functional regression modeling /Fraedaeric Ferraty and Philippe Vieu;Functional linear regression /Hervae Cardot and Pascal Sarda;Linear processes for functional data /Andrae Mas and Besnik Pumo;Kernel regression estimation for functional data /Fraedaeric Ferraty and Philippe Vieu;Nonparametric methods for a(alpha)-mixing functional data /Laurent Delsol;Functional coefficient models for economics and financial data /Zongwu Cai --Part II.Benchmark methods for FDA:Resampling methods for functional data /Timothy McMurry and Dimitris Politis;Principal component analysis for functional data: methodology, theory, and discussion /Peter Hall;Curve registration /James Ramsay;Classification methods for functional data /Amparo Baaillo, Antonio Cuevas, and Ricardo Fraiman;Sparseness and functional data analysis /Gareth James --Part III.Towards a stochastic background in infinite-dimensional spaces:Vector integration and stochastic integration in Banach spaces /Nicolae Dinculeanu;Operator geometry in statistics /Karl Gustafson;On Bernstein type and maximal inequalities for dependent Banach-valued random vectors and applications /Noureddine Rhomari;On product measures associated with stationary processes /Alain Boudou and Yves Romain;An invitation to operator-based statistics /Yves Romain. "As technology progresses, we are able to handle larger and larger datasets. At the same time, monitoring devices such as electronic equipment and sensors (for registering images, temperature, etc.) have become more and more sophisticated. This high-tech revolution offers the opportunity to observe phenomena in an increasingly accurate way by producing statistical units sampled over a finer and finer grid, with the measurement points so close that the data can be considered as observations varying over a continuum. Such continuous (or functional) data may occur in biomechanics (e.g. human movements), chemometrics (e.g. spectrometric curves), econometrics (e.g. the stock market index), geophysics (e.g. spatio-temporal events such as El Nino or time series of satellite images), or medicine (electro-cardiograms/electro-encephalograms). It is well known that standard multivariate statistical analyses fail with functional data. However, the great potential for applications has encouraged new methodologies able to extract relevant information from functional datasets. This Handbook aims to present a state of the art exploration of this high-tech field, by gathering together most of major advances in this area. Leading international experts have contributed to this volume with each chapter giving the key original ideas and comprehensive bibliographical information. The main statistical topics (classification, inference, factor-based analysis, regression modelling, resampling methods, time series, random processes) are covered in the setting of functional data. The twin challenges of the subject are the practical issues of implementing new methodologies and the theoretical techniques needed to expand the mathematical foundations and toolbox. The volume therefore mixes practical, methodological and theoretical aspects of the subject, sometimes within the same chapter. As a consequence, this book should appeal to a wide audience of engineers, practitioners and graduate students, as well as academic researchers, not only in statistics and probability but also in the numerous related application areas"--Provided by publisher.
