Series: Springer Series in Statistics
2006, Approx. 350 p., Hardcover
ISBN: 0-387-40267-5
About this textbook
This book is intended for graduate students in statistics and
industrial mathematics, as well as researchers and practitioners
in the field. We cover both theory and practice of nonparametric
estimation. The text is novel in its use of maximum penalized
likelihood estimation, and the theory of convex minimization
problems (fully developed in the text) to obtain convergence
rates. We also use (and develop from an elementary view point)
discrete parameter submartingales and exponential inequalities. A
substantial effort has been made to discuss computational
details, and to include simulation studies and analyses of some
classical data sets using fully automatic (data driven)
procedures. Some theoretical topics that appear in textbook form
for the first time are definitive treatments of I.J. Good's
roughness penalization, monotone and unimodal density estimation,
asymptotic optimality of generalized cross validation for spline
smoothing and analogous methods for ill-posed least squares
problems, and convergence proofs of EM algorithms for random
sampling problems.
Table of contents
Nonparametric Regression Problems * Asymptotic Optimality of GCV
for Periodic Smoothing Splines * Tikhonov Regularization of Ill-posed
Problems * EM Algorithms for Nonparametric Maximum Likelihood
Estimation Problems * Majorizing Functions and Monotonicity
Properties of EM Algorithms and the Like * Alternating Projection
Methods of Csisz r and Tusn dy
Series: Springer Series in Statistics
2nd ed., 2006, Approx. 680 p., Hardcover
ISBN: 0-387-40087-7
About this book
Statisticians, probabilists, and mathematicians will all be
interested in a expanded version of this classic work on
inequalities. The theory of inequalities has applications in
virtually every branch of mathematics.
Table of contents
Introduction * Doubly Stochastic Matrices * Schur-Convex
Functions * Equivalent Conditions for Majorization * Preservation
and Generation of Majorization * Rearrangements and Majorization
* Combinatorial Analysis * Geometric Inequalities * Matrix Theory
* Numerical Analysis * Stochastic Majorizations * Probabilistic
and Statistical Applications * Additional Statsitical
Applications * Orderings Extending Majorization * Multivariate
Majorization * Convex Functions and Some Classical Inequalities *
Stochastic Ordering * Total Positivity * Matrix Factorizations,
Compounds, Direct Products, and M- Matrices, Extremal
Representations of Matrix Functions
Series: Springer Series in Statistics
Approx. 300 p., Hardcover
ISBN: 0-387-40268-3
About this book
This book states the probabilistic foundations of MCMC algorithms
in a self-contained manner.
Table of contents
Why Do We Need MCMC * MCMC Algorithms * Existence and Invariance
* Irreducibility * Small Sets and Periodicities * Convergence of
Pn * Convergence of Functions * Uniform Convergence * Geometric
Ergodicity * Improved Candidates: Langevin Models * Improved
Candidates: MADA Models * Computable Bounds * Rates of
Convergence of the Gibbs Sampler * Scaling Proposals in MCMC
2006, Approx. 300 p. 5 illus., Hardcover
ISBN: 0-387-40094-X
About this textbook
This book is an introduction to the modern ways of teaching
classical and quantum field theories. A key tool is symmetries.
For the resolution of classical theories, special attention is
given to the definition of advanced or retarded potentials to
ease the understanding of path integrals. The Path integral is
used as the conceptual tool for defining the quantum field
theories. The classical formalism is presented as a useful way to
concretely compute observables that one defines in the path
integral framework. The book contains special chapters which are
devoted to new domains which have not been presented at the
undergraduate level. They include constructive quantum field
theories and topological field theory. This advanced text, which
grew out from a course at famous Ecole Polytechnique, offers a
modern approach to field theory, with exercises, questions and
hints.
Table of contents
Introduction - Relativistic Invariance - The Electromagnetic
Field - Physical States - The Dirac Equation
Series: Springer Texts in Statistics
2006, Approx. 200 p., Softcover
ISBN: 0-387-40273-X
Due: July 2005
About this book
Simulation has become a basic tool for the practice of applied
probability and statistics. The Gibbs Sampler is an especially
important, but not widely understood simulation method. With a
basic introduction to Monte Carlo simulation that provides enough
background in other topics, students can understand the rationale
for and use of the Gibbs Sampler as a practical simulation tool
Table of contents
Pseudorandom Numbers * Screening Tests * Two-State Markov Chains
* Simple Gibbs Sampler * Basics of Bayesian Estimation * Bayesian
Gibbs Sampler * Additional Uses of the Gibbs Sampler
Series: Statistics for Industry and Technology
2006, Approx. 450 p. 40 illus., Hardcover
ISBN: 0-8176-4361-3
A Birkhauser book
Due: August 2005
In this volume, several distinguished and active researchers will
highlight some of the recent developments in statistical
distribution theory, order statistics and their properties, and
some inferential methods associated with them. The volume is
classified into different parts according to the focus of the
articles. Applications of the distributions and inferential
procedures into survival analysis, reliability, quality control,
and environmental problems will be highlighted.
This comprehensive reference work will serve the statistical and
applied mathematics communities as well as practitioners,
researchers and grad students in applied probability and
statistics, reliability engineering, and biostatistics.
Series: Springer Series in Statistics
2005, Approx. 550 p., Softcover
ISBN: 0-387-26142-7
Due: August 2005
About this book
This book presents the contemporary statistical methods and
theory of nonlinear time series analysis. The principal focus is
on nonparametric and semiparametric techniques developed in the
last decade. It covers the techniques for modelling in state-space,
in frequency-domain as well as in time-domain. To reflect the
integration of parametric and nonparametric methods in analyzing
time series data, the book also presents an up-to-date exposure
of some parametric nonlinear models, including ARCH/GARCH models
and threshold models. A compact view on linear ARMA models is
also provided. Data arising in real applications are used
throughout to show how nonparametric approaches may help to
reveal local structure in high-dimensional data. Important
technical tools are also introduced. The book will be useful for
graduate students, application-oriented time series analysts, and
new and experienced researchers. It will have the value both
within the statistical community and across a broad spectrum of
other fields such as econometrics, empirical finance, population
biology and ecology. The prerequisites are basic courses in
probability and statistics. Jianqing Fan, coauthor of the highly
regarded book Local Polynomial Modeling, is Professor of
Statistics at the University of North Carolina at Chapel Hill and
the Chinese University of Hong Kong. His published work on
nonparametric modeling, nonlinear time series, financial
econometrics, analysis of longitudinal data, model selection,
wavelets and other aspects of methodological and theoretical
statistics has been recognized with the Presidents' Award from
the Committee of Presidents of Statistical Societies, the
Hettleman Prize for Artistic and Scholarly Achievement from the
University of North Carolina, and by his election as a fellow of
the American Statistical Association and the Institute of
Mathematical Statistics. Qiwei Yao is Professor of Statistics at
the London School of Economics and Political Science. He is an
elected member of the International Statistical Institute, and
has served on the editorial boards for the Journal of the Royal
Statistical Society (Series B) and the Australian and New Zealand
Journal of Statistics.
Table of contents
Introduction.- Characteristics of Time Series.- ARMA Modeling and
Forecasting.- Parametric Nonlinear Time Series Models.-
Nonparametric Density Estimation.- Smoothing in Time Series.-
Spectral Density Estimation and Its Applications.- Nonparametric
Models.- Model Validation.- Nonlinear Prediction.