Basic Methods of Linear Functional Analysis

Bootstrap methods are computer-intensive methods of statistical analysis, which use simulation to calculate standard errors, confidence intervals, and significance tests. The methods apply for any level of modelling, and so can be used for fully parametric, semiparametric, and completely nonparametric analysis. This 1997 book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. S-Plus programs for implementing the

This concise, application-oriented text is designed to meet the needs of practitioners and students in applied fields in its coverage of major, updated methods in the analysis of survival data. Includ

Over the past 15 years, the availability of cheap and convenient microcomputers has changed the collection methods and analysis of household survey data in developing countries, making the data availa

Numerical Methods in Finance has emerged as a discipline at the intersection of probability theory, finance and numerical analysis. This book, based on lectures given at the Newton Institute as part of a broader programme, describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially of American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures; identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Articles have been written in a pedagogic style and made reasonably self-contained, covering both mathematical matters and practical issues in numerical problems. Thus the book has something to offer economists, probabilists and applied mathematicians working in finance.

Mothers and infants exchanging gleeful vocalizations, married couples discussing their problems, children playing, birds courting and monkeys fighting have this in common: their interactions with others unfold over time. Almost anyone who is interested can observe and describe such phenomena. But usually scientists demand more. They want observations that are replicable and amenable to scientific analysis, while still faithful to the dynamics of the phenomena studied. This book provides a straightforward introduction to scientific methods for observing social behavior. Because of the importance of time in the dynamics of social interaction, sequential approaches to analyzing and understanding social behavior are emphasized. An advanced knowledge of statistical analysis is not required. Instead, the authors present fundamental concepts and offer practical advice.

The book covers a vast array of methods for the analysis of volatile compounds exuded by plants. Some of these volatiles are of great commercial importance, including the aromas of wines and teas, and

Attempts to model the effects of global change are inhibited by a lack of information about how individual plant and animal species will respond. One way of reducing the problem is to develop models treating a smaller number of groups or 'functional types' with similar characteristics. This 1977 book describes approaches and methods for defining these functional types in ways which maximize our potential to predict accurately the responses of real vegetation with real species diversity.

Mathematical Methods in Chemical Engineering builds on students' knowledge of calculus, linear algebra, and differential equations, employing appropriate examples and applications from chemical engine

Mothers and infants exchanging gleeful vocalizations, married couples discussing their problems, children playing, birds courting and monkeys fighting have this in common: their interactions with others unfold over time. Almost anyone who is interested can observe and describe such phenomena. But usually scientists demand more. They want observations that are replicable and amenable to scientific analysis, while still faithful to the dynamics of the phenomena studied. This book provides a straightforward introduction to scientific methods for observing social behavior. Because of the importance of time in the dynamics of social interaction, sequential approaches to analyzing and understanding social behavior are emphasized. An advanced knowledge of statistical analysis is not required. Instead, the authors present fundamental concepts and offer practical advice.

Multivariate statistics refer to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two

This graduate-level text aims to introduce students of the natural sciences to the powerful technique of factor analysis and to provide them with the background necessary to be able to undertake analyses on their own. A thoroughly updated and expanded version of the authors' successful textbook on geological factor analysis, this book draws on examples from botany, zoology, ecology, and oceanography, as well as geology. Applied multivariate statistics has grown into a research area of almost unlimited potential in the natural sciences. The methods introduced in this book, such as classical principal components, principal component factor analysis, principal coordinate analysis, and correspondence analysis, can reduce masses of data to manageable and interpretable form. Q-mode and Q-R-mode methods are also presented. Special attention is given to methods of robust estimation and the identification of atypical and influential observations. Throughout the book, the emphasis is on applicat

Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the 'N-body problem', is a central aspect of many different branches of physics. In recent years, significant advances have been made in the development of fast N-body algorithms to deal efficiently with such complex problems. This book is the first to give a thorough introduction to these so-called 'tree methods', setting out the basic principles and giving many practical examples of their use. No prior specialist knowledge is assumed, and the techniques are illustrated throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modelling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.

Surface analysis deals with the characterisation and understanding of the outer layers of substrates. How they react, look and function are all of interest to the surface scientists. From the basic pr

Ecological theories and hypotheses are usually complex because of natural variability in space and time, which often makes the design of experiments difficult. The statistical tests we use require data to be collected carefully and with proper regard to the needs of these tests. This book, first published in 1996, describes how to design ecological experiments from a statistical basis using analysis of variance, so that we can draw reliable conclusions. The logical procedures that lead to a need for experiments are described, followed by an introduction to simple statistical tests. This leads to a detailed account of analysis of variance, looking at procedures, assumptions and problems. One-factor analysis is extended to nested (hierarchical) designs and factorial analysis. Finally, some regression methods for examining relationships between variables are covered. Examples of ecological experiments are used throughout to illustrate the procedures and examine problems. This book will be

Ecological theories and hypotheses are usually complex because of natural variability in space and time, which often makes the design of experiments difficult. The statistical tests we use require data to be collected carefully and with proper regard to the needs of these tests. This book, first published in 1996, describes how to design ecological experiments from a statistical basis using analysis of variance, so that we can draw reliable conclusions. The logical procedures that lead to a need for experiments are described, followed by an introduction to simple statistical tests. This leads to a detailed account of analysis of variance, looking at procedures, assumptions and problems. One-factor analysis is extended to nested (hierarchical) designs and factorial analysis. Finally, some regression methods for examining relationships between variables are covered. Examples of ecological experiments are used throughout to illustrate the procedures and examine problems. This book will be

The data analytic methods routinely applied in the analysis of recidivism data in criminology have been expanded to include immune individuals. This book describes the theory and methods of incorporat

A rigorous, concise development of the concepts of modern matrix structural analysis, with particular emphasis on the techniques and methods that form the basis of the finite element method. All relev

Essential Environmental Science brings together within a single volume the vast range of techniques, methods and basic tools necessary for the study of the environment. Environmental science has a mas

This 1996 book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strange attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike tra

Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introducti

Providing a comprehensive picture of the design, conduct, analysis, and interpretation of non-experimental studies of both infectious and non-infectious diseases, the Second Edition of this widely use

Advances in computer technology have conveniently coincided with trends in numerical analysis toward increased complexity of computational algorithms based on finite difference methods. It is no longe

A practical, `user-friendly' guide to the issues and methods associated with text and discourse analysis. Text and Discourse Analysis:* examines a wide variety of authentic texts including news storie

This book gives the basis of the probabilistic functional analysis on Wiener space, developed during the last decade. The subject has progressed considerably in recent years thr- ough its links with Q

Taking an informal approach, Hagle presents a review of the basic mathematical concepts that underlie most quantitative analysis in the social sciences. After an algebra review featuring sets and co

The aim of this book is to describe the methods leading to mechanical and numerical modelling of the linear vibrations of elastic structures coupled with internal fluids (sloshing, hydroelasticity and

Ecological data has several special properties: the presence or absence of species on a semi-quantitative abundance scale; non-linear relationships between species and environmental factors; and high inter-correlations among species and among environmental variables. The analysis of such data is important to the interpretation of relationships within plant and animal communities and with their environments. In this corrected version of Data Analysis in Community and Landscape Ecology, without using complex mathematics, the contributors demonstrate the methods that have proven most useful, with examples, exercises and case-studies. Chapters explain in an elementary way powerful data analysis techniques such as logic regression, canonical correspondence analysis, and kriging.

Generations of biologists have relied upon this useful book, which presents the basic concepts of statistics so lucidly and convincingly. It recognises that students must be aware of when to use standard techniques and how to apply the results they obtain. Since many biologists do not have a strong mathematical background, the arguments are gauged in terms which can be easily understood by those with only an elementary knowledge of algebra. Mathematical derivations are avoided and formulae are only used as a convenient shorthand. Although the subject is presented with great simplicity, the coverage is wide and will satisfy the needs of those working in many disciplines. New material for this third edition includes consideration of pocket electronic calculators, and a special chapter is devoted to a discussion of the problems associated with numerical calculation, electronic calculators and computers.

A Practical Guide to Instrumental Analysis covers basic methods of instrumental analysis, including electroanalytical techniques, optical techniques, atomic spectroscopy, X-ray diffraction, thermoanal

This revised and expanded edition emphasizes the basic concepts underlying the analysis and design of all discrete and integrated circuits. Contains an extensive treatment of semiconductor fundamental

International experts from around the globe present a rich variety of intriguing developments in time series analysis in hydrology and environmental engineering. Climatic change is of great concern to

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathematical interest. As with the previous volume, the authors assume a background knowledge of elementary linear algebra and rudimentary analytical concepts. Many examples and exercises of varying difficulty are included.

In Part I the reader is introduced to the methods of measuring the fractal dimension of irregular geometric structures. Part II demonstrates important modern methods for the statistical analysis of ra

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

Factor analysis is a statistical technique widely used in psychology and the social sciences. With the advent of powerful computers, factor analysis and other multivariate methods are now available t

Despite its remote and seemingly rigorous environment, the Antarctic is the world's most important habitat for seals, currently supporting more seals than all other parts of the world combined. As various national Antarctic programmes were established to study these animals, the need to standardize techniques became apparent. This book, arising from work by the Scientific Committee on Antarctic Research (Group of Specialists on Seals), gives a detailed account of well-tried and, where possible, agreed methodologies, techniques, procedures and rationale for the collection and initial analysis of data on the biology and population ecology of Antarctic seals. This volume will not only help facilitate comparisons between different regions of Antarctica, but will also provide a guide for those studying seals in other parts of the world and those carrying out research on other large mammal species.

Intended for coastal engineers and marine scientists who desire to develop a fundamental physical understanding of ocean waves and be able to apply this knowledge to ocean and coastal analysis and des