Bücher der Reihe Lecture Notes in Statistics

This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions.

Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications.

Methods of risk analysis and the outcome of particular evaluations and predictions are covered in detail in this proceedings volume, whose contributions are based on invited presentations from Professor Mei-Ling Ting Lee's 2011 symposium on Risk Analysis and the Evaluation of Predictions.

This book covers a wide range of topics in both discrete and continuous optimal designs. The topics discussed include designs for regression models, covariates models, models with trend effects, and models with competition effects.

Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited.

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Historically, the Gaussian copula model has been one of the most common models in credit risk.

A stochastic process {X(t): 0 S t < =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) > i}, i E S, are increasing (decreasing) with t on T.

The chapters in this volume stress the need for advances in theoretical understanding to go hand-in-hand with the widespread practical application of forecasting in industry.

Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications.

Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.

This volume is a collection of eight Case Studies in Data Analysis that appeared in various issues of the Canadian Journal of Statistics (OS) over a twelve year period from 1982 to 1993.

The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Ito integrals and finally chaotic Wiener-Ito spectral representation of subordinated processes.

In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen.

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory.

This book satisfies this need by a presentation of the spatstat package and many statistical examples.Researchers, spatial statisticians and scientists from biology, geosciences, materials sciences and other fields will use this book as a helpful guide to the application of point process statistics.

This refereed volume includes papers presented at a conference on modelling longitudinal and spatially correlated data. Many of the best researchers in the world have presented papers in an area with important applications to biostatistics and the environmental sciences.

Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data.

The identification of important risk factors and the quantification of risk stemming from an interplay between many risk factors is a prerequisite for mastering the challenges of risk perception, analysis and management successfully.

The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction.

This proceedings volume contains eight selected papers thatwere presented in the International Symposium in Statistics (ISS) 2015 OnAdvances in Parametric and Semi-parametric Analysis of Multivariate, TimeSeries, Spatial-temporal, and Familial-longitudinal Data, held in St. John's,Canada from July 6 to 8, 2015.

Two of the most exciting topics of current research in stochastic networks are the complementary subjects of stability and rare events - roughly, the former deals with the typical behavior of networks, and the latter with significant atypical behavior.

The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms.

Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada.

This book presents the modern theory of nonparametric goodness-of-fit testing. It fills the gap in modern nonparametric statistical theory by discussing hypothesis testing and addresses mathematical statisticians who are interesting in the theory of non-parametric statistical inference.

By providing a comprehensive look at statistical inference from record-breaking data in both parametric and nonparametric settings, this book treats the area of nonparametric function estimation from such data in detail. Statisticians, mathematicians, and engineers will find the book useful as a research reference.

Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.

This work is devoted to several problems of parametric (mainly) and nonparametric estimation through the observation of Poisson processes defined on general spaces. There are a lot of good books on point processes and many of them contain chapters devoted to statistical inference for general and partic ular models of processes.

In the last decade, graphical models have become increasingly popular as a statistical tool. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.

Graphical Methods for Experimental Design presents a strategic view of the planning of experiments, and provides a number of graphical tools that are useful for justifying the effort required for experimentation, identifying variables and candidate statistical models, selecting the set of run conditions and for assessing the quality of the design.