Nonparametric curve estimation: methods, theory and applications

423 Pages·1999·3.279 MB·English

by  Sam Efromovich

springer Series in Statistics
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Sam Efromovich
Nonparametric Curve
Estimation
Methods, Theory, and AppUcations
With 130 Figures
Springer
Sam Efromovich
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, NM 87131-1141
USA
Library of Congress Cataloging-in-Publication Data
Efromovich, Sam.
Nonparametric curve estimation : methods, theory, and applications
/ Sam Efromovich.
p. cm. — (Springer series in statistics)
Includes bibliographical references and index.
ISBN 0-387-98740-1 (hardcover)
1. Nonparametric statistics. 2. Estimation theory. 1. Title.
II. Series.
QA278.8.E35 1999
519.5—dc21 99-13253
© 1999 Springer-Verlag New York, 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-Verlag New York, Inc., 175 Fifth Avenue,
New York, NY 10010, 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, computer software, or by similar or dissimilar methodology now known or here-
after developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even
if the former are not especially identified, is not to be taken as a sign that such names, as
understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely
by anyone.
ISBN 0-387-98740-1 Springer-Verlag New York Berlin Heidelberg SPIN 10709119
To my parents
Preface
Appropriate for a one-semester course, this self-contained book is an in-
troduction to nonparametric curve estimation theory. It may be used for
teachinggraduatestudentsinstatistics(inthiscaseanintermediatecourse
in statistical inference, on the level of the book by Casella and Berger
(1990), is the prerequisite) as well as for diverse classes with students from
other sciences including engineering, business, social, medical, and biolog-
ical among others (in this case a traditional intermediate calculus course
plusanintroductorycourseinprobability,onthelevelofthebookbyRoss
(1997), are the prerequisites).
There are several distinguishing features of this book that should be
highlighted:
-Allbasicstatisticalmodels,includingprobabilitydensityestimation,non-
parametric regression, time series analysis including spectral analysis, and
filtering of time-continuous signals, are considered as one general problem.
As a result, universal methods of estimation are discussed, and students
become familiar with a wide spectrum of applications of nonparametric
methods.
- Main emphasis is placed on the case of small sample sizes and data-
driven orthogonal series estimates (Chapters 1–6). Chapter 7 discusses
(with proofs) modern asymptotic results, and Chapter 8 is devoted to a
thorough discussion of nonseries methods.
- The companion software package (available over the World Wide Web)
allowsstudentstoproduceandmodifyalmostallfiguresofthebookaswell
as to analyze a broad spectrum of simulated and real data sets. Based on
the S–PLUS environment, this package requires no knowledge of S–PLUS
viii Preface
and is elementary to use. Appendix B explains how to install and use this
package;italsocontainsinformationabouttheaffordableS–PLUSStudent
Edition for PC.
-“PracticalSeminar”sectionsaredevotedtoapplyingthemethodsstudied
to the analysis and presentation of real data sets. The software for these
sections allows students to analyze any data set that exists in the S–PLUS
environment.
- “Case Study” sections allow students to explore applications of basic
methods to more complicated practical problems. These sections together
with “Special Topic” sections give the instructor some flexibility in choos-
ing additional material beyond the core.
- Plenty of exercises with different levels of difficulty will allow the
instructor to keep students with different mathematical and statistical
backgrounds out of trouble!
-“Notes”sectionsattheendofeachchapterareprimarilydevotedtobooks
for further reading. They also capture some bibliographic comments, side
issues, etc.
- Appendix A contains a brief review of fundamentals of statistical in-
ference. All the related notions and notations used in the book may be
found there. It is highly recommended to review these fundamentals prior
to studying Chapters 3–8. Also, exercises for Appendix A may be used as
a first quiz or homework.
Abitofadvicetothereaderwhowouldliketousethisbookforself-study
and who is venturing for the first time into this area. You can definitely
just read this book as any other text without using the companion soft-
ware. There are plenty of figures (more than a hundred), which will guide
you through the text. However, if you have decided to study nonparamet-
rics, then you are probably interested in data analysis. I cannot stress too
strongly the importance of combining reading with analyzing both simu-
lated and real data sets. This is the kind of experience that you can gain
only via repeated exercises, and here the software can make this process
dramatically quicker and less painful. Using the software will allow you to
check virtually every claim and development mentioned in the book and
make the material fully transparent. Also, please review the fundamentals
outlined in Appendix A prior to studying Chapters 3–8.
All further developments related to this book will be posted on the
WWW page http://www.math.unm.edu/∼efrom/book1, and the author
may be contacted by electronic mail as [e-mail].
Acknowledgments
I would like to thank everyone who in various ways has had influence on
thisbook.MybiggestthanksgotoMarkPinsker.AlexSamarovgraciously
read and gave comments on a draft of the book. John Kimmel provided
Preface ix
invaluable assistance through the publishing process. Three “generations”
ofmystudentswhotooktheclassonnonparametriccurveestimationbased
on this book shared with me their thoughts, comments, and suggestions. I
thank all of you.
Sam Efromovich
Albuquerque, USA, 1999