Projecting Statistical Functionals
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Projecting Statistical Functionals
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Author : Tomasz Rychlik
language : en
Publisher:
Release Date : 2001
Projecting Statistical Functionals written by Tomasz Rychlik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Projecting Statistical Functionals
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Author : Tomasz Rychlik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Projecting Statistical Functionals written by Tomasz Rychlik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
About 10 years ago I began studying evaluations of distributions of or der statistics from samples with general dependence structure. Analyzing in [78] deterministic inequalities for arbitrary linear combinations of order statistics expressed in terms of sample moments, I observed that we obtain the optimal bounds once we replace the vectors of original coefficients of the linear combinations by the respective Euclidean norm projections onto the convex cone of vectors with nondecreasing coordinates. I further veri fied that various optimal evaluations of order and record statistics, derived earlier by use of diverse techniques, may be expressed by means of projec tions. In Gajek and Rychlik [32], we formulated for the first time an idea of applying projections onto convex cones for determining accurate moment bounds on the expectations of order statistics. Also for the first time, we presented such evaluations for non parametric families of distributions dif ferent from families of arbitrary, symmetric, and nonnegative distributions. We realized that this approach makes it possible to evaluate various func tionals of great importance in applied probability and statistics in different restricted families of distributions. The purpose of this monograph is to present the method of using pro jections of elements of functional Hilbert spaces onto convex cones for es tablishing optimal mean-variance bounds of statistical functionals, and its wide range of applications. This is intended for students, researchers, and practitioners in probability, statistics, and reliability.
Statistical Matching
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Author : Susanne Rässler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Matching written by Susanne Rässler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Data fusion or statistical file matching techniques merge data sets from different survey samples to solve the problem that exists when no single file contains all the variables of interest. Media agencies are merging television and purchasing data, statistical offices match tax information with income surveys. Many traditional applications are known but information about these procedures is often difficult to achieve. The author proposes the use of multiple imputation (MI) techniques using informative prior distributions to overcome the conditional independence assumption. By means of MI sensitivity of the unconditional association of the variables not jointy observed can be displayed. An application of the alternative approaches with real world data concludes the book.
Statistics On Special Manifolds
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Author : Yasuko Chikuse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-12
Statistics On Special Manifolds written by Yasuko Chikuse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Mathematics categories.
The special manifolds of interest in this book are the Stiefel manifold and the Grassmann manifold. Formally, the Stiefel manifold Vk,m is the space of k frames in the m-dimensional real Euclidean space Rm, represented by the set of m x k matrices X such that X' X = I , where Ik is the k x k identity matrix, k and the Grassmann manifold Gk,m-k is the space of k-planes (k-dimensional hyperplanes) in Rm. We see that the manifold Pk,m-k of m x m orthogonal projection matrices idempotent of rank k corresponds uniquely to Gk,m-k. This book is concerned with statistical analysis on the manifolds Vk,m and Pk,m-k as statistical sample spaces consisting of matrices. The discussion is carried out on the real spaces so that scalars, vectors, and matrices treated in this book are all real, unless explicitly stated otherwise. For the special case k = 1, the observations from V1,m and G1,m-l are regarded as directed vectors on a unit sphere and as undirected axes or lines, respectively. There exists a large literature of applications of directional statis tics and its statistical analysis, mostly occurring for m = 2 or 3 in practice, in the Earth (or Geological) Sciences, Astrophysics, Medicine, Biology, Meteo rology, Animal Behavior, and many other fields. Examples of observations on the general Grassmann manifold Gk,m-k arise in the signal processing of radar with m elements observing k targets.
Order Statistics
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Author : Herbert A. David
language : en
Publisher: John Wiley & Sons
Release Date : 2004-03-22
Order Statistics written by Herbert A. David and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Mathematics categories.
This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones.
Dependence In Probability And Statistics
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Author : Paul Doukhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Dependence In Probability And Statistics written by Paul Doukhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.
This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.
Spatial Statistics And Computational Methods
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Author : Jesper Møller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Spatial Statistics And Computational Methods written by Jesper Møller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Spatial statistics and Markov Chain Monte Carlo (MCMC) techniques have each undergone major developments in the last decade. Also, these two areas are mutually reinforcing, because MCMC methods are often necessary for the practical implementation of spatial statistical inference, while new spatial stochastic models in turn motivate the development of improved MCMC algorithms. This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It consists of four chapters: 1. Petros Dellaportas and Gareth O. Roberts give a tutorial on MCMC methods, the computational methodology which is essential for virtually all the complex spatial models to be considered in subsequent chapters. 2. Peter J. Diggle, Paulo J, Ribeiro Jr., and Ole F. Christensen introduce the reader to the model- based approach to geostatistics, i.e. the application of general statistical principles to the formulation of explicit stochastic models for geostatistical data, and to inference within a declared class of models. 3. Merrilee A. Hurn, Oddvar K. Husby, and H?vard Rue discuss various aspects of image analysis, ranging from low to high level tasks, and illustrated with different examples of applications. 4. Jesper Moller and Rasmus P. Waggepetersen collect recent theoretical advances in simulation-based inference for spatial point processes, and discuss some examples of applications. The volume introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers. It is partly based on the course material for the "TMR and MaPhySto Summer School on Spatial Statistics and Computational Methods," held at Aalborg University, Denmark, August 19-22, 2001.
Case Studies In Bayesian Statistics
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Author : Constantine Gatsonis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Case Studies In Bayesian Statistics written by Constantine Gatsonis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The 5th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University campus on September 24-25, 1999. As in the past, the workshop featured both invited and contributed case studies. The former were presented and discussed in detail while the latter were presented in poster format. This volume contains the three invited case studies with the accompanying discussion as well as ten contributed pa pers selected by a refereeing process. The majority of case studies in the volume come from biomedical research. However, the reader will also find studies in education and public policy, environmental pollution, agricul ture, and robotics. INVITED PAPERS The three invited cases studies at the workshop discuss problems in ed ucational policy, clinical trials design, and environmental epidemiology, respectively. 1. In School Choice in NY City: A Bayesian Analysis ofan Imperfect Randomized Experiment J. Barnard, C. Frangakis, J. Hill, and D. Rubin report on the analysis of the data from a randomized study conducted to evaluate the New YorkSchool Choice Scholarship Pro gram. The focus ofthe paper is on Bayesian methods for addressing the analytic challenges posed by extensive non-compliance among study participants and substantial levels of missing data. 2. In Adaptive Bayesian Designs for Dose-Ranging Drug Trials D. Berry, P. Mueller, A. Grieve, M. Smith, T. Parke, R. Blazek, N.
Case Studies In Bayesian Statistics 6 2002
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Author : Constantine Gatsonis
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-12
Case Studies In Bayesian Statistics 6 2002 written by Constantine Gatsonis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-12 with Mathematics categories.
This volume contains invited case studies with the accompanying discussion as well as contributed papers selected by a refereeing process of 6th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University in October, 2001.
Advances In Distribution Theory Order Statistics And Inference
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Author : N. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-23
Advances In Distribution Theory Order Statistics And Inference written by N. Balakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-23 with Mathematics categories.
Barry Arnold has made fundamental contributions to many different areas of statistics, including distribution theory, Bayesian inference, multivariate analysis, bounds and orderings, and characterization problems. Organized to honor Arnold’s significant contributions to the field, this volume is an outgrowth of the "International Conference on Distribution Theory, Order Statistics, and Inference," held at the University of Cantabria, Santander, Spain. Several distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized. This comprehensive reference work will serve the statistical and applied mathematics communities, as well as practitioners, researchers, and graduate students in applied probability and statistics, reliability engineering, and biostatistics.