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Analytical spaces --- Topology --- Normed linear spaces --- 517.982 --- 515.12 --- #WWIS:ALTO --- Linear normed spaces --- Normed vector spaces --- Banach spaces --- Functional analysis --- Vector analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Linear spaces with topology and order or other structures --- General topology --- Normed linear spaces. --- Topology. --- 515.12 General topology --- 517.982 Linear spaces with topology and order or other structures
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Almost as soon as we had completed our previous book Functional Data Analysis in 1997, it became clear that potential interest in the field was far wider than the audience for the thematic presentation we had given there. At the same time, both of us rapidly became involved in relevant new research involving many colleagues in fields outside statistics. This book treats the field in a different way, by considering case stories arising from our own collaborative research to illustrate how functional data analysis ideas work out in practice in a diverse range of subject areas. These include criminology, economics, archaeology, rheumatology, psychology, neurophysiology, auxology (the study of human growth), meteorology, biomechanics, and education—and also a study of a juggling statistician. Obviously such an approach will not cover the field exhaustively, and in any case functional data analysis is not a hard-edged closed system of thought. Nevertheless we have tried to give a flavor of the range of methodology we ourselves have considered. We hope that our personal experience, including the fun we had working on these projects, will inspire others to extend “functional” thinking to many other statistical contexts. Of course, many of our case studies required development of existing methodology, and readers should gain the ability to adapt methods to their own problems too.
Multivariate analysis --- Mathematical statistics --- Statistics. --- Statistical Theory and Methods. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Statistics for Social Science, Behavioral Science, Education, Public Policy, and Law. --- Multivariate analysis. --- Mathematical statistics. --- Statistics for Social Sciences, Humanities, Law. --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- Statistics . --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics
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Scientists and others today often collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modeling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology, much of it based on the authors’ own research work, while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. This second edition is aimed at a wider range of readers, and especially those who would like to apply these techniques to their research problems. It complements the authors' other recent volume Applied Functional Data Analysis: Methods and Case Studies. In particular, there is an extended coverage of data smoothing and other matters arising in the preliminaries to a functional data analysis. The chapters on the functional linear model and modeling of the dynamics of systems through the use of differential equations and principal differential analysis have been completely rewritten and extended to include new developments. Other chapters have been revised substantially, often to give more weight to examples and practical considerations. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He was President of the Statistical Society of Canada in 2002-3 and holds the Society’s Gold Medal for his work in functional data analysis. Bernard Silverman is Master of St Peter’s College and Professor of Statistics at Oxford University. He was President of the Institute of Mathematical Statistics in 2000–1. He is a Fellow of the Royal Society. His main specialty is in computational statistics, and he is the author or editor of several highly regarded books in this area. .
Multivariate analysis --- Multivariate analysis. --- Mathematical statistics --- Multivariate Analysis. --- Analyse multivariée --- EPUB-LIV-FT SPRINGER-B --- Mathematical statistics. --- Statistical Theory and Methods. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- 519.2 --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- 519.5 --- EPUB-LIV-FT SPRINGER-B LIVSTATI --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics
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