Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverm....pdf-资料库

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第1页.png

第1页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第2页.png

第2页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第3页.png

第3页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第4页.png

第4页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第5页.png

第5页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第6页.png

第6页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第7页.png

第7页 / 共431页

ymhblue-2409715-Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverman).pdf-第8页.png

第8页 / 共431页

Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger

J.O. Ramsay B.W. Silverman Functional Data Analysis Second Edition With 151 Illustrations

J.O. Ramsay Department of Psychology University of Montreal Montreal, Quebec H3A 1B1 Canada ramsay@psych.mcgill.ca B.W. Silverman St. Peter’s College Oxford OX1 2DL United Kingdom bernard.silverman@spc.ox.ac.uk Library of Congress Control Number: 2005923773 Printed on acid-free paper. ISBN-10: 0-387-40080-X ISBN-13: 978-0387-40080-8 © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring St., New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, com- puter software, or by similar or dissimilar methodology now known or hereafter developed is for- bidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. (MP) 9 8 7 6 5 4 3 2 1 springeronline.com

J.O. Ramsay Department of Psychology McGill University Montreal, Quebec H4A 1B1 Canada ramsay@psych.mcgill.ca B.W. Silverman St. Peter’s College Oxford OX1 2DL United Kingdom bernard.silverman@spc.ox.ac.uk Library of Congress Control Number: 2005923773 Printed on acid-free paper. ISBN-10: 0-387-40080-X ISBN-13: 978-0387-40080-8 © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring St., New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, com- puter software, or by similar or dissimilar methodology now known or hereafter developed is for- bidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. (MP) 9 8 7 6 5 4 3 2 1 springeronline.com

Preface to the Second Edition This book continues in the footsteps of the First Edition in being a snap- shot of a highly social, and therefore decidedly unpredictable, process. The combined personal view of functional data analysis that it presents has emerged over a number of years of research and contact, and has been greatly nourished by delightful collaborations with many friends. We hope that readers will enjoy the book as much as we have enjoyed writing it, whether they are our colleagues as researchers or applied data analysts reading the book as a research monograph, or students using it as a course text. As in the First Edition, live data 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. “Back to the data” was the heading to the last section of the First Edi- tion. We did not know then how well those words would predict the next eight years. Since then we have seen functional data applications in more scientiﬁc and industrial settings than we could have imagined, and so we wanted an opportunity to make this new ﬁeld accessible to a wider reader- ship than the the ﬁrst volume seemed to permit. Our book of case studies, Ramsay and Silverman (2002), was our ﬁrst response, but we have known for some time that a new edition of our original volume was also required. We have added a considerable amount of new material, and considered carefully how the original material should be presented. One main objec-

vi tive has been, especially when introducing the various concepts, to provide more intuitive discussion and to postpone needless mathematical terminol- ogy where possible. In addition we wanted to oﬀer more practical advice on the processing of functional data. To this end, we have added a more extended account of spline basis functions, provided new material on data smoothing, and extended the range of ways in which data can be used to estimate functions. In response to many requests, we have added some proposals for estimating conﬁdence regions, highlighting local features, and even testing hypotheses. Nevertheless, the emphasis in the revision remains more exploratory and conﬁrmatory. Our treatment of the functional linear model in the First Edition was only preliminary, and since then a great deal of work has been done on this topic by many investigators. A complete overhaul of this material was called for, and the chapters on linear modelling have been completely re- worked. On the other hand, our coverage of principal components analysis and canonical correlation still seems appropriate, and not much has been changed. Readers reacted to the later chapters on diﬀerential equations as being diﬃcult, and so we have tried to make them a friendlier place to be. In some places we have opted for an ‘intuitive’ rather than ‘rigorous’ approach. This is not merely because we want our book to be widely acces- sible; in our view the theoretical underpinnings of functional data analysis still require rather more study before a treatment can be written that will please theoreticians. We hope that the next decade will see some exciting progress in this regard. We both believe that a good monograph is a personal view rather than a dry encyclopedia. The average of two personal views is inevitably going to be less ‘personal’ than either of the two individual views, just as the average of a set of functions may omit detail present in the original functions. To counteract this tendency, we have ensured that everything we say in our informal and intuitive discussion of certain issues is the view of at least one of us, but we have not always pressed for unanimous agreement! We owe so much to those who helped us to go here. We would like to repeat our thanks to those who helped with the First Edition: Michal Abra- hamowicz, Philippe Besse, Darrell Bock, Catherine Dalzell, Shelly Feran, Randy Flanagan, Rowena Fowler, Theo Gasser, Mary Gauthier, Vince Gracco, Nancy Heckman, Anouk Hoedeman, Steve Hunka, Iain Johnstone, Alois Kneip, Wojtek Krzanowski, Xiaochun Li, Kevin Munhall, Guy Na- son, Richard Olshen, David Ostry, Tim Ramsay, John Rice and Xiaohui Wang. We also continue our grateful acknowledgement of ﬁnancial support from the Natural Science and Engineering Research Council of Canada, the National Science Foundation and the National Institute of Health of the USA, and the British Engineering and Physical Sciences Research Council. The seed for the First Edition, and therefore for the Revised Edition as well, was planted at a discussion meeting of the Royal Statistical Society

vii Research Section, where one of us read a paper and the other proposed the vote of thanks, not always an occasion that leads to a meeting of minds! Turning to the Second Edition, Soﬁa Mosesova and Yoshio Takane read the entire manuscript with an eye to the technical correctness as well as the readability of what they saw, and caught us on many points. David Camp- bell helped with the literature review that supported our “Further readings and notes” sections. Time spent at the University of British Columbia made possible many stimulating conversations with Nancy Heckman and her col- leagues. A discussion of many issues with Alois Kneip as well his hospitality for the ﬁrst author at the University of Mainz was invaluable. The oppor- tunity for us to spend time together aﬀorded by St Peter’s College and the Department of Statistics at Oxford University was essential to the project. April 2005 Jim Ramsay & Bernard Silverman

Contents Preface to the Second Edition 1 Introduction 1.1 What are functional data? . . . . . . . . . . . . . . . . . Functional models for nonfunctional data . . . . . . . . . 1.2 Some functional data analyses . . . . . . . . . . . . . . . 1.3 The goals of functional data analysis 1.4 . . . . . . . . . . . 1.5 The ﬁrst steps in a functional data analysis . . . . . . . . 1.5.1 Data representation: smoothing and interpolation 1.5.2 Data registration or feature alignment . . . . . . 1.5.3 Data display . . . . . . . . . . . . . . . . . . . . . 1.5.4 Plotting pairs of derivatives . . . . . . . . . . . . Exploring variability in functional data . . . . . . . . . . 1.6.1 Functional descriptive statistics . . . . . . . . . . 1.6.2 Functional principal components analysis . . . . . 1.6.3 Functional canonical correlation . . . . . . . . . . Functional linear models . . . . . . . . . . . . . . . . . . Using derivatives in functional data analysis . . . . . . . Concluding remarks . . . . . . . . . . . . . . . . . . . . . 1.7 1.8 1.9 1.6 2 Tools for exploring functional data 2.1 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Some notation . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Scalars, vectors, functions and matrices . . . . . . v 1 1 5 5 9 11 11 12 13 13 15 15 15 16 16 17 18 19 19 20 20

资料库

Functional Data Analysis Second Edition(J.O. Ramsay,B.W. Silverm....pdf

相关推荐

开发技术

热门标签

最新资料