Approx. 335 p. 25 illus. 2003 Approx. 335
p. 25 illus.
Hardcover
0-387-00928-0
This book gives a detailed account of bootstrap
methods and their
properties for dependent data, covering a
wide range of topics
such as block bootstrap methods, bootstrap
methods in the
frequency domain, resampling methods for
long range dependent
data, and resampling methods for spatial
data. The first five
chapters of the book treat the theory and
applications of block
bootstrap methods at the level of a graduate
text. The rest of
the book is written as a research monograph,
with frequent
references to the literature, but mostly
at a level accessible to
graduate students familiar with basic concepts
in statistics.
Supplemental background material is added
in the discussion of
such important issues as second order properties
of bootstrap
methods, bootstrap under long range dependence,
and bootstrap for
extremes and heavy tailed dependent data.
Further, illustrative
numerical examples are given all through
the book and issues
involving application of the methodology
are discussed. The book
fills a gap in the literature covering research
on resampling
methods for dependent data that has witnessed
vigorous growth
over the last two decades but remains scattered
in various
statistics and econometrics journals. It
can be used as a
graduate level text for a special topics
course on resampling
methods for dependent data and also as a
research monograph for
statisticians and econometricians who want
to learn more about
the topic and want to apply the methods in
their own research. S.N.
Lahiri is a professor of Statistics at the
Iowa State University,
is a Fellow of the Institute of Mathematical
Statistics and a
Fellow of the American Statistical Association.
Contents:
Scope of Resampling Methods for Dependent
Data.- Bootstrap
Methods.- Properties of Block Bootstrap Methods
for the Sample
Mean.- Extensions and Examples.- Comparison
of Block Bootstrap
Methods.- Model Based Bootstrap.- Frequency
Domain Bootstrap.-
Long Range Dependence.- Resampling Methods
for Spatial Data.-
Special Topics.
Series: Springer Series in Statistics.
2003 Approx. 250 p. 25 illus., 7 in color.
Hardcover
0-387-40122-9
Lie groups, Lie algebras, and representation
theory are the main
focus of this text. In order to keep the
prerequisites to a
minimum, the author restricts attention to
matrix Lie groups and
Lie algebras. This approach keeps the discussion
concrete, allows
the reader to get to the heart of the subject
quickly, and covers
all of the most interesting examples. The
book also introduces
the often-intimidating machinery of roots
and the Weyl group in a
gradual way, using examples and representation
theory as
motivation. The text is divided into two
parts. The first covers
Lie groups and Lie algebras and the relationship
between them,
along with basic representation theory. The
second part covers
the theory of semisimple Lie groups and Lie
algebras, beginning
with a detailed analysis of the representations
of SU(3). The
author illustrates the general theory with
numerous images
pertaining to Lie algebras of rank two and
rank three, including
images of root systems, lattices of dominant
integral weights,
and weight diagrams. This book is sure to
become a standard
textbook for graduate students in mathematics
and physics with
little or no prior exposure to Lie theory.
Brian Hall is an
Associate Professor of Mathematics at the
University of Notre
Dame.
Contents:
Preface.- I: General Theory: Matrix Lie Groups;
Lie Algebras and
the Exponential Mapping; The Baker-Campbell-Hausdorff
Formula;
Basic Representation Theory.- II: Semisimple
Theory: The
Representations of SU(3); Semisimple Lie
Algebras;
Representations of Complex Semisimple Lie
Algebras; More on Roots
and Weights.- Appendix A: A Quick Introduction
to Groups.-
Appendix B: Linear Algebra Review.- Appendix
C: More on Lie
Groups.- Appendix D: Clebsch-Gordan Theory
for SU(2) and the
Wigner-Eckart Theorem.- Appendix E: Computing
Fundamental Groups
of Matrix Lie Groups.- Bibliography.
Series: Graduate Texts in Mathematics. Vol..
222
2003 Approx. 288 p. 24 illus. Hardcover
0-387-00836-5
This book presents the basic ideas in Fourier
analysis and its
applications to the study of partial differential
equations. It
also covers the Laplace and Zeta transformations
and the
fundaments of their applications. The author
has intended to make
his exposition accessible to readers with
a limited background,
for example, those not acquainted with the
Lebesgue integral or
with analytic functions of a complex variable.
At the same time,
he has included discussions of more advanced
topics such as the
Gibbs phenomenon, distributions, Sturm-Liouville
theory, Cesaro
summability and multi-dimensional Fourier
analysis, topics which
one usually will not find in books at this
level.
Many of the chapters end with a summary of
their contents, as
well as a short historical note. The text
contains a great number
of examples, as well as more than 350 exercises.
In addition, one
of the appendices is a collection of the
formulas needed to solve
problems in the field.
Anders Vretblad is Senior Lecturer of Mathematics
at Uppsala
University, Sweden.
Contents:
Introduction * Preparations * Laplace and
Z Transforms * Fourier
Series * L^2 Theory * Separation of Variables
* Fourier
Transforms * Distributions * Multi-Dimentional
Fourier Analysis *
Appendix A: The ubiquitous convolution *
Appendix B: The Discrete
Fourier Transform * Appendix C: Formulae
* Appendix D: Answers to
exercises * Appendix E: Literature
Series: Graduate Texts in Mathematics. Vol..
223
2003 Approx. 335 p. 38 illus. Hardcover
0-387-40401-5
In the past three decades, bifurcation theory
has matured into a
well-established and vibrant branch of mathematics.
This book
gives a unified presentation in an abstract
setting of the main
theorems in bifurcation theory, as well as
more recent and lesser
known results. It covers both the local and
global theory of one-parameter
bifurcations for operators acting in infinite-dimensional
Banach
spaces, and shows how to apply the theory
to problems involving
partial differential equations. In addition
to existence,
qualitative properties such as stability
and nodal structure of
bifurcating solutions are treated in depth.
This volume will
serve as an important reference for mathematicians,
physicists,
and theoretically-inclined engineers working
in bifurcation
theory and its applications to partial differential
equations.
Contents: Introduction.- Local Theory.- Global
Theory.-
Applications.
Series: Applied Mathematical Sciences. Vol..
156
2003 Approx. 200 p. 58 illus. Hardcover
0-387-40081-8
Statistical Tools for Nonlinear Regression,
Second Edition,
presents methods for analyzing data using
parametric nonlinear
regression models. The new edition has been
expanded to include
binomial, multinomial and Poisson non-linear
models. Using
examples from experiments in agronomy and
biochemistry, it shows
how to apply these methods. It concentrates
on presenting the
methods in an intuitive way rather than developing
the
theoretical backgrounds. The examples are
analyzed with the free
software nls2 updated to deal with the new
models included in the
second edition. The nls2 package is implemented
in S-PLUS and R.
Its main advantages are to make the model
building, estimation
and validation tasks, easy to do. More precisely,
Complex models
can be easily described using a symbolic
syntax. The regression
function as well as the variance function
can be defined
explicitly as functions of independent variables
and of unknown
parameters or they can be defined as the
solution to a system of
differential equations. Moreover, constraints
on the parameters
can easily be added to the model. It is thus
possible to test
nested hypotheses and to compare several
data sets. Several
additional tools are included in the package
for calculating
confidence regions for functions of parameters
or calibration
intervals, using classical methodology or
bootstrap. Some
graphical tools are proposed for visualizing
the fitted curves,
the residuals, the confidence regions, and
the numerical
estimation procedure.
Contents:
Nonlinear regression model and parameter
estimation.- Accuracy of
estimators, confidence intervals and tests.-
Variance estimation.-
Diagnostics of model misspecification.- Calibration
and
prediction.- Binomial non-linear models.-
Multinomial and Poisson
non-linear models.
Series: Springer Series in Statistics.