Download or read book Statistical Applications of Jordan Algebras written by James D. Malley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.

Download or read book Jordan Canonical Form written by Steven H. Weintraub and published by Morgan & Claypool Publishers. This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it-eigenvalues, eigenvectors, and chains of generalized eigenvectors. We begin with the diagonalizable case and then proceed to the general case, but we do not present a complete proof. Indeed, our interest here is not in JCF per se, but in one of its important applications. We devote the bulk of our attention in this book to showing how to apply JCF to solve systems of constant-coefficient first order differential equations, where it is a very effective tool. We cover all situations-homogeneous and inhomogeneous systems; real and complex eigenvalues. We also treat the closely related topic of the matrix exponential. Our discussion is mostly confined to the 2-by-2 and 3-by-3 cases, and we present a wealth of examples that illustrate all the possibilities in these cases (and of course, exercises for the reader). Table of Contents: Jordan Canonical Form / Solving Systems of Linear Differential Equations / Background Results: Bases, Coordinates, and Matrices / Properties of the Complex Exponential

Download or read book Statistical Modelling and Risk Analysis written by Christos P. Kitsos and published by Springer Nature. This book was released on 2024-01-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the latest results on novel methods in Risk Analysis and assessment, with applications in Biostatistics (which is providing food for thought since the first ICRAs, covering traditional areas of RA, until now), Engineering Reliability, the Environmental Sciences and Economics. The contributions, based on lectures given at the 9th International Conference on Risk Analysis (ICRA 9), at Perugia, Italy, May 2022, detail a wide variety of daily risks, building on ideas presented at previous ICRA conferences. Working within a strong theoretical framework, supporting applications, the material describes a modern extension of the traditional research of the 1980s. This book is intended for graduate students in Mathematics, Statistics, Biology, Toxicology, Medicine, Management, and Economics, as well as quantitative researchers in Risk Analysis.

Download or read book Innovations in Industrial Engineering written by José Machado and published by Springer Nature. This book was released on 2021-06-23 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a variety of topics in the field of industrial engineering, with a special focus on research and industrial applications aimed at both improving quality of processes and products and contributing to a sustainable economy. Based on a set of papers presented at the 1st International Conference “Innovation in Engineering”, ICIE, held in Guimarães, Portugal, on June 28–30, 2021, it focuses on innovative technologies associated with and strategies for the development of Industry 4.0. The chapters discuss new ways to improve industrial production and supply chain management by applying mathematical and computational methods. They also cover important issues relating to sustainability, education, and collaborations between industry and universities, and national developments. This book, which belongs to a three-volume set, provides engineering researchers and professionals with a timely overview and extensive information on trends and technologies behind the current and future developments of Industry 4.0.

Download or read book Jordan Structures in Lie Algebras written by Antonio Fernández López and published by American Mathematical Soc.. This book was released on 2019-08-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself.

Download or read book Riesz Probability Distributions written by Abdelhamid Hassairi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a useful overview of results in multivariate probability distributions and multivariate analysis as well as a reference to harmonic analysis on symmetric cones adapted to the needs of researchers in analysis and probability theory.

Download or read book Lundberg Approximations for Compound Distributions with Insurance Applications written by Gordon E. Willmot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The basic technique employed in the derivation of many bounds is induc tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.

Download or read book Applications of Computer Aided Time Series Modeling written by Masanao Aoki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of three parts: Part One is composed of two introductory chapters. The first chapter provides an instrumental varible interpretation of the state space time series algorithm originally proposed by Aoki (1983), and gives an introductory account for incorporating exogenous signals in state space models. The second chapter, by Havenner, gives practical guidance in apply ing this algorithm by one of the most experienced practitioners of the method. Havenner begins by summarizing six reasons state space methods are advanta geous, and then walks the reader through construction and evaluation of a state space model for four monthly macroeconomic series: industrial production in dex, consumer price index, six month commercial paper rate, and money stock (Ml). To single out one of the several important insights in modeling that he shares with the reader, he discusses in Section 2ii the effects of sampling er rors and model misspecification on successful modeling efforts. He argues that model misspecification is an important amplifier of the effects of sampling error that may cause symplectic matrices to have complex unit roots, a theoretical impossibility. Correct model specifications increase efficiency of estimators and often eliminate this finite sample problem. This is an important insight into the positive realness of covariance matrices; positivity has been emphasized by system engineers to the exclusion of other methods of reducing sampling error and alleviating what is simply a finite sample problem. The second and third parts collect papers that describe specific applications.

Download or read book Wavelets Approximation and Statistical Applications written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process ing. Five years ago wavelet theory progressively appeared to be a power ful framework for nonparametric statistical problems. Efficient computa tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available software code. We hope therefore to address both theory and practice with this book and thus help to construct bridges between the different groups of scientists. This te. xt grew out of a French-German cooperation (Seminaire Paris Berlin, Seminar Berlin-Paris). This seminar brings together theoretical and applied statisticians from Berlin and Paris. This work originates in the first of these seminars organized in Garchy, Burgundy in 1994.

Download or read book Projecting Statistical Functionals written by Tomasz Rychlik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results are recent, and a significant part of them has not been published yet. Numerous open problems are stated in the text.

Download or read book Case Studies in Bayesian Statistics written by Constantine Gatsonis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of case studies presents detailed applications of Bayesian statistical analysis, emphasising the scientific context. The papers were presented and discussed at a workshop held at Carnegie-Mellon University, and this volume - dedicated to the memory of Morrie Groot-reproduces six invited papers, each with accompanying invited discussion, and nine contributed papers with the focus on econometric applications.

Download or read book Elements of Statistical Disclosure Control written by Leon Willenborg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical disclosure control is the discipline that deals with producing statistical data that are safe enough to be released to external researchers. This book concentrates on the methodology of the area. It deals with both microdata (individual data) and tabular (aggregated) data. The book attempts to develop the theory from what can be called the paradigm of statistical confidentiality: to modify unsafe data in such a way that safe (enough) data emerge, with minimum information loss. This book discusses what safe data, are, how information loss can be measured, and how to modify the data in a (near) optimal way. Once it has been decided how to measure safety and information loss, the production of safe data from unsafe data is often a matter of solving an optimization problem. Several such problems are discussed in the book, and most of them turn out to be hard problems that can be solved only approximately. The authors present new results that have not been published before. The book is not a description of an area that is closed, but, on the contrary, one that still has many spots awaiting to be more fully explored. Some of these are indicated in the book. The book will be useful for official, social and medical statisticians and others who are involved in releasing personal or business data for statistical use. Operations researchers may be interested in the optimization problems involved, particularly for the challenges they present. Leon Willenborg has worked at the Department of Statistical Methods at Statistics Netherlands since 1983, first as a researcher and since 1989 as a senior researcher. Since 1989 his main field of research and consultancy has been statistical disclosure control. From 1996-1998 he was the project coordinator of the EU co-funded SDC project.

Download or read book Stochastic Epidemic Models and Their Statistical Analysis written by Hakan Andersson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture notes describe stochastic epidemic models and methods for their statistical analysis. Our aim is to present ideas for such models, and methods for their analysis; along the way we make practical use of several probabilistic and statistical techniques. This will be done without focusing on any specific disease, and instead rigorously analyzing rather simple models. The reader of these lecture notes could thus have a two-fold purpose in mind: to learn about epidemic models and their statistical analysis, and/or to learn and apply techniques in probability and statistics. The lecture notes require an early graduate level knowledge of probability and They introduce several techniques which might be new to students, but our statistics. intention is to present these keeping the technical level at a minlmum. Techniques that are explained and applied in the lecture notes are, for example: coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm and MCMC methods. The aim is to introduce and apply these techniques, thus hopefully motivating their further theoretical treatment. A few sections, mainly in Chapter 5, assume some knowledge of weak convergence; we hope that readers not familiar with this theory can understand the these parts at a heuristic level. The text is divided into two distinct but related parts: modelling and estimation.

Download or read book General Theory of Statistics written by Victor Aladjev and published by Fultus Corporation. This book was released on 2004 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book Description The present book is a statistical course for undergraduate students in all fields of social and economic sciences. The book presents a manual on the course "General Theory of Statistics", including a series of not quite traditional topics. First of all, it concerns the mathematical bases of statistics and use of computer technologies in statistical probing. Thematic choice of the chapters and sections of the book is caused not only by interests and tastes of the authors, but also by modern tendencies in applied statistics and orientation of the given work. The book is based on a course of lectures given by the first author for undergraduates in social and economic sciences along with three books published in Russian and English in Estonia, Lithuania and Byelorussia. This book has been written for a large enough audience of teachers, researchers, statisticians, students, collegians and users of statistics in behavioral and social sciences. Above all, the book is directed to a wide circle of the readers studying statistical disciplines in high schools and colleges; however, it can be useful also to persons independently studying statistics. Author Biography (Aladjev V.Z.) Professor Aladjev V.Z. was born on June 14, 1942 in the town Grodno (Byelorussia). Now, he is the First vice-president of the International Academy of Noosphere and the president of Tallinn Research Group, whose scientific results have received international recognition, first, in the field of mathematical theory of Cellular Automata (CA). He is member of a series of Russian and International Academies. Aladjev V. Z. is the author of more than 330 scientific publications, including 63 books, published in many countries. He participates as a member of the organizing committee and/or a guest lecturer in many international scientific forums in mathematics and cybernetics. Author Biography (Haritonov V.N.) Dr. Haritonov V.N. was born on August 2, 1946 in the town Nizhni Novgorod (Russia). On successful graduation from Tallinn Technical University, he has acquired a profession of economics. Since 1972, Haritonov V.N. has the respectable positions in the Estonian banking system. Now, he is the Chairman of the Board of Tallinn Business Bank. Most considerable methodological projects and practical results of Haritonov V.N. are related to economic sciences, and, above all, to banking field, including automation of banking system, banking statistics, etc. Along with a series of publications, Haritonov V.N. has participated in many scientific and applied forums on banking economics.

Download or read book Wavelets and Statistics written by Anestis Antoniadis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its short history, wavelet theory has found applications in a remarkable diversity of disciplines: mathematics, physics, numerical analysis, signal processing, probability theory and statistics. The abundance of intriguing and useful features enjoyed by wavelet and wavelet packed transforms has led to their application to a wide range of statistical and signal processing problems. On November 16-18, 1994, a conference on Wavelets and Statistics was held at Villard de Lans, France, organized by the Institute IMAG-LMC, Grenoble, France. The meeting was the 15th in the series of the Rencontres Pranco-Belges des 8tatisticiens and was attended by 74 mathematicians from 12 different countries. Following tradition, both theoretical statistical results and practical contributions of this active field of statistical research were presented. The editors and the local organizers hope that this volume reflects the broad spectrum of the conference. as it includes 21 articles contributed by specialists in various areas in this field. The material compiled is fairly wide in scope and ranges from the development of new tools for non parametric curve estimation to applied problems, such as detection of transients in signal processing and image segmentation. The articles are arranged in alphabetical order by author rather than subject matter. However, to help the reader, a subjective classification of the articles is provided at the end of the book. Several articles of this volume are directly or indirectly concerned with several as pects of wavelet-based function estimation and signal denoising.

Download or read book Statistical Disclosure Control in Practice written by Leon Willenborg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to discuss various aspects associated with disseminating personal or business data collected in censuses or surveys or copied from administrative sources. The problem is to present the data in such a form that they are useful for statistical research and to provide sufficient protection for the individuals or businesses to whom the data refer. The major part of this book is concerned with how to define the disclosure problem and how to deal with it in practical circumstances.

Download or read book Non Regular Statistical Estimation written by Masafumi Akahira and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.