Statistics with Vague Data

Theory and Decision Library B

Book 6
Springer Science & Business Media
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This monograph is an attempt to unify existing works in the field of random sets, random variables, and linguistic random variables with respect to statistical analysis. It is intended to be a tutorial research compendium. The material of the work is mainly based on the postdoctoral thesis (Ha bilitationsschrift) of the first author and on several papers recently published by both authors. The methods form the basis of a user-friendly software tool which supports the statistical inferenee in the presence of vague data. Parts of the manuscript have been used in courses for graduate level students of mathematics and eomputer scienees held by the first author at the Technical University of Braunschweig. The textbook is designed for readers with an advanced knowledge of mathematics. The idea of writing this book came from Professor Dr. H. Skala. Several of our students have significantly contributed to its preparation. We would like to express our gratitude to Reinhard Elsner for his support in typesetting the book, Jorg Gebhardt and Jorg Knop for preparing the drawings, Michael Eike and Jiirgen Freckmann for implementing the programming system and Giinter Lehmann and Winfried Boer for proofreading the manuscript. This work was partially supported by the Fraunhofer-Gesellschaft. We are indebted to D. Reidel Publishing Company for making the pub lication of this book possible and would especially like to acknowledge the support whieh we received from our families on this project.
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Springer Science & Business Media
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Dec 6, 2012
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Business & Economics / Operations Research
Computers / Computer Science
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
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This volume contains the Proceedings of the Advanced Symposium on Multivariate Modeling and Data Analysis held at the 64th Annual Heeting of the Virginia Academy of Sciences (VAS)--American Statistical Association's Vir ginia Chapter at James Madison University in Harrisonburg. Virginia during Hay 15-16. 1986. This symposium was sponsored by financial support from the Center for Advanced Studies at the University of Virginia to promote new and modern information-theoretic statist ical modeling procedures and to blend these new techniques within the classical theory. Multivariate statistical analysis has come a long way and currently it is in an evolutionary stage in the era of high-speed computation and computer technology. The Advanced Symposium was the first to address the new innovative approaches in multi variate analysis to develop modern analytical and yet practical procedures to meet the needs of researchers and the societal need of statistics. vii viii PREFACE Papers presented at the Symposium by e1l11lJinent researchers in the field were geared not Just for specialists in statistics, but an attempt has been made to achieve a well balanced and uniform coverage of different areas in multi variate modeling and data analysis. The areas covered included topics in the analysis of repeated measurements, cluster analysis, discriminant analysis, canonical cor relations, distribution theory and testing, bivariate densi ty estimation, factor analysis, principle component analysis, multidimensional scaling, multivariate linear models, nonparametric regression, etc.
This volume contains most of the invited and contributed papers presented at the Conference on Robustness of Statistical Methods and Nonparametric Statistics held in the castle oj'Schwerin, Mai 29 - June 4 1983. This conference was organized by the Mathematical Society of the GDR in cooperation with the Society of Physical and Mathematical Biology of the GDR, the GDR-Region of the International Biometric Society and the Academy of Agricultural Sciences of the GDR. All papers included were thoroughly reviewed by scientist listed under the heading "Editorial Collabora tories·'. Some contributions, we are sorry to report, were not recommended for publi cation by the rf'vif'wers and do not appear in these proceedings. The editors thank the reviewers for their valuable comments and suggestions. The conference was organizf'd bv a Programme Committee, its chairman was Prof. Dr. Dieter Rasch (Research Centre of Animal Production, Dummerstorf-Rostock). The members of the Programme Committee were Prof. Dr., Johannes Adam (Martin-Luther-University Halle) Prof. Dr. Heinz Ahrens (Academy of Sciences of the GDR, Berlin) Doz. Dr. Jana Jureckova (Charles University Praha) Prof. Dr. Moti Lal Tiku (McMaster University, Hamilton, Ontario) The aim of the conference was to discuss several aspects of robustness but mainly to present new results regarding the robustness of classical statistical methods especially tests, confidence estimations, and selection procedures, and to compare their perfor mance with nonparametric procedures. Robustness in this sens~ is understood as intensivity against. violation of the normal assumption.
We are glad to present the proceedings of the 5th biennial conference in the Intelligent Data Analysis series. The conference took place in Berlin, Germany, August 28–30, 2003. IDA has by now clearly grown up. Started as a small si- symposium of a larger conference in 1995 in Baden-Baden (Germany) it quickly attractedmoreinterest(bothsubmission-andattendance-wise),andmovedfrom London (1997) to Amsterdam (1999), and two years ago to Lisbon. Submission ratesalongwiththeeverimprovingqualityofpapershaveenabledtheor- nizers to assemble increasingly consistent and high-quality programs. This year we were again overwhelmed by yet another record-breaking submission rate of 180 papers. At the Program Chairs meeting we were – based on roughly 500 reviews – in the lucky position of carefully selecting 17 papers for oral and 42 for poster presentation. Poster presenters were given the opportunity to summarize their papers in 3-minute spotlight presentations. The oral, spotlight and poster presentations were then scheduled in a single-track, 2. 5-day conference program, summarized in this book. In accordance with the goal of IDA, “to bring together researchers from diverse disciplines,” we achieved a nice balance of presentations from the more theoreticalside(bothstatisticsandcomputerscience)aswellasmoreapplicati- oriented areas that illustrate how these techniques can be used in practice. Work presented in these proceedings ranges from theoretical contributions dealing, for example, with data cleaning and compression all the way to papers addressing practical problems in the areas of text classi?cation and sales-rate predictions. A considerable number of papers also center around the currently so popular applications in bioinformatics.
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