Eggermont, Paul, LaRiccia, Vincent

Maximum Penalized Likelihood Estimation
Regression

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

Marshall, Albert W., Olkin, Ingram, Arnold, Barry

Inequalities: Theory of Majorization and Its Applications

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

Roberts, Gareth O., Tweedie, Richard L.

Understanding Monte Carlo Markov Chain

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

Seneor, Roland, Baulieu, Laurent, Iliopoulos, Jean

From Classical to Quantum Fields
An Introduction to the Path Integral Formalism

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


Suess, Eric A., Trumbo, Bruce E.

Gibbs Sampling and Screening Tests
From Random Numbers to the Gibbs Sampler

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

Balakrishnan, N.; Castillo, Enrique; Maria Sarabia, Jose (Eds.)

Advances in Distributions, Order Statistics, and Inference

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.


Fan, Jianqing, Yao, Qiwei

Nonlinear Time Series
Nonparametric and Parametric Methods

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.