Synopsis
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 Niño 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.
About the Author
Frédéric Ferraty is a researcher in Statistics at Toulouse University (France). He has been working on all facets of Statistics, ranging from fundamental theory basis, methodology developments to practical implementation. In addition, most of major topics of Statistics as Classification, Exploratory Methods, Regression, Time Series have been investigated. In the last decade, he mainly oriented his research towards high dimensional statistical problems involving systematically functional data. His numerous statistical contributions have been published in prestigious international statistical journals. He is also a prominent and very active member of the international statistical community through co-organizations of several international scientific events and numerous editorial works for publishers and statistical journals of high scientific level.
Yves Romain is an academic researcher at Institute of Mathematics of Toulouse (France). He is Doctor in Applied Mathematics and HDR in Statistics. His main research domains are multivariate analyses in large dimension and related fields such as operator-based statistics and backgrounds for statistics in infinite-dimensional spaces.
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