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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.

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models.

From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years.

The product of a high-flying summer school in Paris in 2009, this volume synthesises the state of the art on ill-posed statistical inverse problems and high-dimensional estimation and explores the ways these techniques can be applied to economics.

Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.

This book gives a comprehensive introduction to exponential family nonlinear models, which are the natural extension of generalized linear models and normal nonlinear regression models. The differential geometric framework is presented for these models and the geometric methods are widely used in this book.

This book will be of interest to mathematical statisticians and biometricians interested in block designs. After presenting the general theory of analysis based on the randomization model in Part I, the constructional and combinatorial properties of design are described in Part II.

This concise, easy-to-follow book stimulates interest and develops proficiency in statistical analysis.

This book outlines and demonstrates problems with the use of the HP filter, and proposes an alternative strategy for inferring cyclical behavior from a time series featuring seasonal, trend, cyclical and noise components.

Covering statistical analysis on the two special manifolds, the Stiefel manifold and the Grassmann manifold, this book is designed as a reference for both theoretical and applied statisticians.

Robust Bayesian analysis aims at overcoming the traditional objection to Bayesian analysis of its dependence on subjective inputs, mainly the prior and the loss.

In order to precisely model real-life systems or man-made devices, both nonlinear and dynamic properties need to be taken into account.

A title that arises from the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place March 2010. It details developments, methods and applications in spatial statistics and related areas.

This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm).

This book contains papers based on these presentations, as well as vignettes provided by Paul Holland before each section.The papers in this book attest to how Paul Holland's pioneering ideas influenced and continue to influence several fields such as social networks, causal inference, item response theory, equating, and DIF.

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.

Random Effect and Latent Variable Model Selection In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of ?elds.

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.

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.

This collection of papers provides an up to date treatment of item response theory, an important topic in educational testing.

This volume contains a selection of chapters based on papers to be presented at the Fifth Statistical Challenges in Modern Astronomy Symposium. Modern astronomical research faces a vast range of statistical issues which have spawned a revival in methodological activity among astronomers.

These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability.

These nine papers cover three different areas for longitudinal data analysis, four dealing with longitudinal data subject to measurement errors, four on incomplete longitudinal data analysis, and the last one for inferences for longitudinal data subject to outliers.

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.

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.

This revised book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. Variants on these expansions, including much of modern likelihood theory, are discussed and applications to lattice distributions are extensively treated.

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.