Download or read book Infinitely Divisible Statistical Experiments written by Arnold Janssen and published by . This book was released on 1985 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Infinitely Divisible Statistical Experiments written by Arnold Janssen and published by . This book was released on 1985-05-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Infinitely Divisible Statistical Experiments written by Arnold Janssen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Infinitely Divisible Distributions in Statistical Inference Heavy Tailed Distributions and Convolution Models written by Stanley L. Sclove and published by . This book was released on 1976 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The family of infinitely divisible distributions is shown to provide alternative formulations in several inferential situations. In particular, the family provides heavy-tailed distributions and distributions for use in models involving convolutions, such as signal-plus-noise models. Characterizations of sub-families of the infinitely divisible family are used to obtain statistical tests of membership in those sub-families. Special attention is given to the normal and normal-plus-Poisson sub-families. (Author).

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 Nonparametric Statistics for Stochastic Processes written by Denis Bosq and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.

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.

Download or read book Pivotal Measures in Statistical Experiments and Sufficiency written by Sakutaro Yamada and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present work I want to show a mathematical study of the statistical notion of sufficiency mainly for undominated statistical experiments. The famous Burkholder's (1961) and Pitcher's(1957) examples motivated some researchers to develop new theory of sufficiency. Le Cam (1964) is probably the most excellent paper in this field of study. This note also belongs to the same area. Though it is more restrictive than Le Cam's paper(1964), a study which is connected more directly with the classical papers of Halmos and Savage(1949) , and Bahadur(1954) is shown. Namely I want to develop a study based on the notion of pivotal measure which was introduced by Halmos and Savage(1949) . It is great pleasure to have this opportunity to thank Professor H. Heyer and Professor H. Morimoto for their careful reading the manuscript and valuable comments on it. I am also thankful to Professor H. Luschgy and Professor D. Mussmann for thei r proposal of wr i ting "the note". I would like to dedicate this note to the memory of my father Eizo.

Download or read book Extreme Value Theory and Applications written by J. Galambos and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice.

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 The Matching Methodology Some Statistical Properties written by Prem K. Goel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incomplete-data problems arise naturally in many instances of statistical practice. One class of incomplete-data problems, which is relatively not well understood by statisticians, is that of merging micro-data files. Many Federal agencies use the methodology of file-merging to create comprehensive files from multiple but incomplete sources of data. The main objective of this endeavor is to perform statistical analyses on the synthetic data set generated by file merging. In general, these analyses cannot be performed by analyzing the incomplete data sets separately. The validity and the efficacy of the file-merging methodology can be assessed by means of statistical models underlying the mechanisms which may generate the incomplete files. However, a completely satisfactory and unified theory of file-merging has not yet been developed This monograph is only a minor attempt to fill this void for unifying known models. Here, we review the optimal properties of some known matching strategies and derive new results thereof. However, a great number of unsolved problems still need the attention of very many researchers. One main problem still to be resolved is the development of appropriate inference methodology from merged files if one insists on using file merging methodology. If this monograph succeeds in attracting just a few more mathematical statisticians to work on this class of problems, then we will feel that our efforts have been successful.

Download or read book Asymptotic Methods in Probability and Statistics with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2001-06-21 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Download or read book 2 Inverses and Their Statistical Application written by Albert J. Getson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of the traditional approach to linear model analysis is bound up in complex matrix expressions revolving about the usual generalized inverse. Motivated by this important role of the generalized inverse. the research summarized here began as an interest in understanding. in geometric terms. the four conditions defining the qnique Moore-Penrose Inverse. Such an investigation. it was hoped. might lead to a better understanding. and possibly a simplification of. the usual matrix expressions. Initially this research was begun by Francis Hsuan and Pat Langenberg, without knowledge of Kruskal's paper published in 1975. This oversight was perhaps fortu nate. since if they had read his paper they may not have continued their effort. A summary of this early research appears in Hsuan. Langenberg and Getson (1985). This monograph is a summary of the research on {2}-inverses continued by Al Getson. while a graduate student. in collaboration with Francis Hsuan of the Depart ment of Statistics. School of Business Administration. at Temple University. Philadelphia. The literature on generalized inverses and related topics is extensive and some of what is present here has appeared elsewhere. Generally. this literature is not presented from the point of view of {2}-inverses. We have tried to do justice to . the relevant published works and appologize for those we have either overlooked or possibly misrepresented.

Download or read book Statistical Information and Likelihood written by D. Basu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is an honor to be asked to write a foreword to this book, for I believe that it and other books to follow will eventually lead to a dramatic change in the current statistics curriculum in our universities. I spent the 1975-76 academic year at Florida State University in Tallahassee. My purpose was to complete a book on Statistical Reliability Theory with Frank Proschan. At the time, I was working on total time on test processes. At the same time, I started attending lectures by Dev Basu on statistical inference. It was Lehmann's hypothesis testing course and Lehmann's book was the text. However, I noticed something strange - Basu never opened the book. He was obviously not following it. Instead, he was giving a very elegant, measure theoretic treatment of the concepts of sufficiency, ancillarity, and invariance. He was interested in the concept of information - what it meant. - how it fitted in with contemporary statistics. As he looked at the fundamental ideas, the logic behind their use seemed to evaporate. I was shocked. I didn't like priors. I didn't like Bayesian statistics. But after the smoke had cleared, that was all that was left. Basu loves counterexamples. He is like an art critic in the field of statistical inference. He would find a counterexample to the Bayesian approach if he could. So far, he has failed in this respect.

Download or read book Learning from Data written by Doug Fisher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years ago Bill Gale of AT&T Bell Laboratories was primary organizer of the first Workshop on Artificial Intelligence and Statistics. In the early days of the Workshop series it seemed clear that researchers in AI and statistics had common interests, though with different emphases, goals, and vocabularies. In learning and model selection, for example, a historical goal of AI to build autonomous agents probably contributed to a focus on parameter-free learning systems, which relied little on an external analyst's assumptions about the data. This seemed at odds with statistical strategy, which stemmed from a view that model selection methods were tools to augment, not replace, the abilities of a human analyst. Thus, statisticians have traditionally spent considerably more time exploiting prior information of the environment to model data and exploratory data analysis methods tailored to their assumptions. In statistics, special emphasis is placed on model checking, making extensive use of residual analysis, because all models are 'wrong', but some are better than others. It is increasingly recognized that AI researchers and/or AI programs can exploit the same kind of statistical strategies to good effect. Often AI researchers and statisticians emphasized different aspects of what in retrospect we might now regard as the same overriding tasks.

Download or read book Topics in Infinitely Divisible Distributions and L vy Processes Revised Edition written by Alfonso Rocha-Arteaga and published by Springer Nature. This book was released on 2019-11-02 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L∞ generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.

Download or read book Nonparametric Regression Analysis of Longitudinal Data written by Hans-Georg Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reviews some of the work that has been done for longitudi nal data in the rapidly expanding field of nonparametric regression. The aim is to give the reader an impression of the basic mathematical tools that have been applied, and also to provide intuition about the methods and applications. Applications to the analysis of longitudinal studies are emphasized to encourage the non-specialist and applied statistician to try these methods out. To facilitate this, FORTRAN programs are provided which carry out some of the procedures described in the text. The emphasis of most research work so far has been on the theoretical aspects of nonparametric regression. It is my hope that these techniques will gain a firm place in the repertoire of applied statisticians who realize the large potential for convincing applications and the need to use these techniques concurrently with parametric regression. This text evolved during a set of lectures given by the author at the Division of Statistics at the University of California, Davis in Fall 1986 and is based on the author's Habilitationsschrift submitted to the University of Marburg in Spring 1985 as well as on published and unpublished work. Completeness is not attempted, neither in the text nor in the references. The following persons have been particularly generous in sharing research or giving advice: Th. Gasser, P. Ihm, Y. P. Mack, V. Mammi tzsch, G . G. Roussas, U. Stadtmuller, W. Stute and R.