Weighted Empirical Processes in Dynamic Linear Models

A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these to

A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these to

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes possible the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves. Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics as well as those with an interest in applications, to such area

State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in

This book presents a unified approach for obtaining the limiting distributions of minimum distance. It discusses classes of goodness-of-t tests for fitting an error distribution in some of these model

Although many of the models commonly used in empirical finance are linear, the nature of financial data suggests that non-linear models are more appropriate for forecasting and accurately describing returns and volatility. The enormous number of non-linear time series models appropriate for modeling and forecasting economic time series models makes choosing the best model for a particular application daunting. This classroom-tested advanced undergraduate and graduate textbook, first published in 2000, provides a rigorous treatment of recently developed non-linear models, including regime-switching and artificial neural networks. The focus is on the potential applicability for describing and forecasting financial asset returns and their associated volatility. The models are analysed in detail and are not treated as 'black boxes'. Illustrated using a wide range of financial data, drawn from sources including the financial markets of Tokyo, London and Frankfurt.

Although many of the models commonly used in empirical finance are linear, the nature of financial data suggests that non-linear models are more appropriate for forecasting and accurately describing returns and volatility. The enormous number of non-linear time series models appropriate for modeling and forecasting economic time series models makes choosing the best model for a particular application daunting. This classroom-tested advanced undergraduate and graduate textbook, first published in 2000, provides a rigorous treatment of recently developed non-linear models, including regime-switching and artificial neural networks. The focus is on the potential applicability for describing and forecasting financial asset returns and their associated volatility. The models are analysed in detail and are not treated as 'black boxes'. Illustrated using a wide range of financial data, drawn from sources including the financial markets of Tokyo, London and Frankfurt.

First published in 1983, this book describes the construction and in-laboratory use of basic earth-science equipment, including the flume, rainfall simulator, wind tunnel and wave generator. It is emphasised throughout that the equipment should be capable of a high level of control so that experiments can be planned and replicated. The aim of the book is to facilitate the laboratory study of landform processes in courses associated with geomorphology, geology, physical geography and earth science in general. The book contains details of a number of experiments using each type of simulator, and these are described in detail on a formal objective-procedure-conclusion basis, each conclusion being repeated using a 'systems analysis' approach to key attributes. This book will be invaluable to instructions at universities, colleges and secondary schools who teach earth science, geology, physical geography and geomorphology, and to students training to be teachers in these subjects.

"Understanding the mathematical modeling of chemical processes is fundamental to the successful career of a researcher in chemical engineering. This book reviews, introduces, and develops the mathemat

An integrated work in two volumes, this text teaches readers to formulate, analyze, and evaluate Markov models. The first volume treats basic process; the second, semi-Markov and decision processes. 1

This is a book on stochastic dynamic macroeconomics from a Keynesian perspective. It shows that including Keynesian features in intertemporal models considerably contributes to resolve major puzzles

Introduction to sequential decision processes covers use of dynamic programming in studying models of resource allocation, methods for approximating solutions of control problems in continuous time, p

This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response

This book discusses the understanding that the process of transmission of an infectious disease is not necessarily linear and is dynamical in character. This concept compels the appropriate quantifica

An insightful approach to the analysis of variance in the study of linear models Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis

Written by one of the leading experts in the field, this book focuses on the interplay between model specification, data collection, and econometric testing of dynamic asset pricing models. The first

Chaotic dynamic systems and non-linear processes, together with the resulting fractals and multifractals, are fundamental for analyzing data and understanding processes in the Earth and Environmental

This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes cl

Drug resistance in cancer, whereby a proportion of cancer cells evades chemotherapy, poses a profound and continuing challenge for the effective treatment of cancer. The principles underlying the biological mechanisms behind this phenomenon are clearly understood and explained in this volume. However, a deeper understanding of drug resistance requires a quantitative appreciation of the dynamic forces that shape tumour growth, including spontaneous mutation and selection processes. The authors seek to explain and to simplify these complex mechanisms, and to place them in a clinical context. Clearly explained mathematical models are used to illustrate the biological principles and provide an insight into tumour development and the effectiveness and limitations of drug treatment. It is suitable for those with a non-mathematical background and aims to enhance the effectiveness of cancer therapy.

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Drug resistance in cancer, whereby a proportion of cancer cells evades chemotherapy, poses a profound and continuing challenge for the effective treatment of cancer. The principles underlying the biological mechanisms behind this phenomenon are clearly understood and explained in this volume. However, a deeper understanding of drug resistance requires a quantitative appreciation of the dynamic forces that shape tumour growth, including spontaneous mutation and selection processes. The authors seek to explain and to simplify these complex mechanisms, and to place them in a clinical context. Clearly explained mathematical models are used to illustrate the biological principles and provide an insight into tumour development and the effectiveness and limitations of drug treatment. It is suitable for those with a non-mathematical background and aims to enhance the effectiveness of cancer therapy.

The dynamic development of various processes is a central problem of biology and indeed of all the sciences. The mathematics describing that development is, in general, complicated, because the models that are realistic are usually nonlinear. Consequently many biologists may not notice a possible application of theory. They may be unable to decide whether a particular model captures the essence of a system, or to appreciate that analysis of a model can reveal important aspects of biological problems and may even describe in detail how a system works. The aim of this textbook is to remedy the situation by adopting a general approach to model analysis and applying it several times to problems (drawn primarily from molecular and cellular biology) of gradually increasing biological and mathematical complexity. Although material of considerable sophistication is included, little mathematical background is required - only some exposure to elementary calculus; appendixes supply the necessary

This Element discusses how shiny, an R package, can help instructors teach quantitative methods more effectively by way of interactive web apps. The interactivity increases instructors' effectiveness by making students more active participants in the learning process, allowing them to engage with otherwise complex material in an accessible, dynamic way. The Element offers four detailed apps that cover two fundamental linear regression topics: estimation methods (least squares, maximum likelihood) and the classic linear regression assumptions. It includes a summary of what the apps can be used to demonstrate, detailed descriptions of the apps' full capabilities, vignettes from actual class use, and example activities. Two other apps pertain to a more advanced topic (LASSO), with similar supporting material. For instructors interested in modifying the apps, the Element also documents the main apps' general code structure, highlights some of the more likely modifications, and goes through

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

LEAD will develop you as a leader in a dynamic way that goes to the heart of your purpose and dreams. It takes you well beyond traditional, fixed planning processes, which are out of date as soon as t

This volume of lecture notes for a one-term course reviews the standard approaches to demand estimation used in empirical industrial organization and introduces new methods for estimating dynamic

Addressing all aspects of the design, modeling and simulation of chromatographic processes, this result-oriented primer provides a practical guide to all the necessary approaches, methodologies and tools. Beginning with key definitions and concepts, it builds up from the most simple to the most complex situations, including multicomponent systems, non-uniform velocity profiles, bed instability, particle size distributions, and the influence of complex environments on chromatographic process design. In addition to covering classical approaches, it introduces efficient tools for investigating chromatographic processes, such as the 'Russian-Lego' approach for linear systems, phenomenological models, and specific shortcuts for deriving the key properties of industrial processes. With an emphasis on real-world problems and applications, step-by step modeling design guidelines, and detailed exercises for self-assessment, this is a must-have guide for practitioners and researchers working in

This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly

Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistic

This comprehensive volume on ergodic control for diffusions highlights intuition alongside technical arguments. A concise account of Markov process theory is followed by a complete development of the fundamental issues and formalisms in control of diffusions. This then leads to a comprehensive treatment of ergodic control, a problem that straddles stochastic control and the ergodic theory of Markov processes. The interplay between the probabilistic and ergodic-theoretic aspects of the problem, notably the asymptotics of empirical measures on one hand, and the analytic aspects leading to a characterization of optimality via the associated Hamilton–Jacobi–Bellman equation on the other, is clearly revealed. The more abstract controlled martingale problem is also presented, in addition to many other related issues and models. Assuming only graduate-level probability and analysis, the authors develop the theory in a manner that makes it accessible to users in applied mathematics, engineerin

Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. This book is designed to be a basic one-stop reference for graduate students and researchers. It is based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Thus Part I is a broad introduction to the history, development and philosophy of data assimilation, illustrated by examples; Part II considers the classical, static approaches, both linear and nonlinear; and Part III describes

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

The core of ths book presents a theory developed by the author to combine the recent insight into empirical data with mathematical models in freeway traffic research based on dynamical non-linear proc

Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimat