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Elsevier

Academic Press

  • Mathematical Statistics

    A Decision Theoretic Approach
    • 1st Edition
    • Thomas S. Ferguson
    • Z. W. Birnbaum + 1 more
    • English
    Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.

  • Nonparametric Functional Estimation

    • 1st Edition
    • B. L. S. Prakasa Rao
    • Z. W. Birnbaum + 1 more
    • English
    Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.

  • Information Theory

    Coding Theorems for Discrete Memoryless Systems
    • 1st Edition
    • Imre Csiszár + 1 more
    • Z. W. Birnbaun + 1 more
    • English
    Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon’s information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science.

  • Strong Approximations in Probability and Statistics

    • 1st Edition
    • M. Csörgo + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students.

  • Multivariate Statistical Inference

    • 1st Edition
    • Narayan C. Giri
    • Z. W. Birnbaum + 1 more
    • English
    Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

  • Measure and Integral

    • 1st Edition
    • Konrad Jacobs
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

  • Martingale Limit Theory and Its Application

    • 1st Edition
    • P. Hall + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

  • Stochastic Integration

    • 1st Edition
    • Michel Metivier + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.

  • Writing Reaction Mechanisms in Organic Chemistry

    • 3rd Edition
    • Kenneth A. Savin
    • English
    Writing Reaction Mechanisms in Organic Chemistry, Third Edition, is a guide to understanding the movements of atoms and electrons in the reactions of organic molecules. Expanding on the successful book by Miller and Solomon, this new edition further enhances your understanding of reaction mechanisms in organic chemistry and shows that writing mechanisms is a practical method of applying knowledge of previously encountered reactions and reaction conditions to new reactions. The book has been extensively revised with new material including a completely new chapter on oxidation and reduction reactions including stereochemical reactions. It is also now illustrated with hundreds of colorful chemical structures to help you understand reaction processes more easily. The book also features new and extended problem sets and answers to help you understand the general principles and how to apply these to real applications. In addition, there are new information boxes throughout the text to provide useful background to reactions and the people behind the discovery of a reaction. This new edition will be of interest to students and research chemists who want to learn how to organize what may seem an overwhelming quantity of information into a set of simple general principles and guidelines for determining and describing organic reaction mechanisms.

  • Strategies and Tactics in Organic Synthesis

    • 1st Edition
    • Volume 10
    • Michael Harmata
    • English
    A classic in the area of organic synthesis, Strategies and Tactics in Organic Synthesis provides a forum for investigators to discuss their approach to the science and art of organic synthesis. Rather than a simple presentation of data or a secondhand analysis, we are given stories that vividly demonstrate the power of the human endeavor known as organic synthesis and the creativity and tenacity of its practitioners. Firsthand accounts of each project tell of the excitement of conception, the frustration of failure and the joy experienced when either rational thought or good fortune gives rise to the successful completion of a project. This book series shows how synthesis is really done, and we are educated, challenged and inspired by these accounts, which portray the idea that triumphs do not come without challenges. We also learn that we can meet challenges to further advance the science and art of organic synthesis, driving it forward to meet the demands of society, in discovering new reactions, creating new designs and building molecules with atom and step economies that provide solutions through function to create a better world.

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