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STATISTICS: Textbooks and Monographs D. B. Owen Founding Editor, 1972–1991 Associate Editors Statistical Computing/ Nonparametric Statistics Professor William R. Schucany Southern Methodist University Probability Professor Marcel F. Neuts University of Arizona Multivariate Analysis Professor Anant M. Kshirsagar University of Michigan Quality Control/Reliability Professor Edward G. Schilling Rochester Institute of Technology Editorial Board Applied Probability Dr. Paul R. Garvey The MITRE Corporation Statistical Process Improvement Professor G. Geoffrey Vining Virginia Polytechnic Institute Economic Statistics Professor David E. A. Giles University of Victoria Stochastic Processes Professor V. Lakshmikantham Florida Institute of Technology Survey Sampling Professor Lynne Stokes Southern Methodist University Time Series Sastry G. Pantula North Carolina State University Experimental Designs Mr. Thomas B. Barker Rochester Institute of Technology Multivariate Analysis Professor Subir Ghosh University of California, Riverside Statistical Distributions Professor N. Balakrishnan McMaster University © 2006 by Taylor & Francis Group, LLC

STATISTICS: Textbooks and Monographs Recent Titles Statistical Process Monitoring and Optimization, edited by Sung H. Park and G. Geoffrey Vining Statistics for the 21st Century: Methodologies for Applications of the Future, edited by C. R. Rao and Gábor J. Székely Probability and Statistical Inference, Nitis Mukhopadhyay Handbook of Stochastic Analysis and Applications, edited by D. Kannan and V. Lakshmikantham Testing for Normality, Henry C. Thode, Jr. Handbook of Applied Econometrics and Statistical Inference, edited by Aman Ullah, Alan T. K. Wan, and Anoop Chaturvedi Visualizing Statistical Models and Concepts, R. W. Farebrother and Michaël Schyns Financial and Actuarial Statistics: An Introduction, Dale S. Borowiak Nonparametric Statistical Inference, Fourth Edition, Revised and Expanded, Jean Dickinson Gibbons and Subhabrata Chakraborti Computer-Aided Econometrics, edited by David E.A. Giles The EM Algorithm and Related Statistical Models, edited by Michiko Watanabe and Kazunori Yamaguchi Multivariate Statistical Analysis, Second Edition, Revised and Expanded, Narayan C. Giri Computational Methods in Statistics and Econometrics, Hisashi Tanizaki Applied Sequential Methodologies: Real-World Examples with Data Analysis, edited by Nitis Mukhopadhyay, Sujay Datta, and Saibal Chattopadhyay Handbook of Beta Distribution and Its Applications, edited by Arjun K. Gupta and Saralees Nadarajah Item Response Theory: Parameter Estimation Techniques, Second Edition, edited by Frank B. Baker and Seock-Ho Kim Statistical Methods in Computer Security, edited by William W. S. Chen Elementary Statistical Quality Control, Second Edition, John T. Burr Data Analysis of Asymmetric Structures, Takayuki Saito and Hiroshi Yadohisa Mathematical Statistics with Applications, Asha Seth Kapadia, Wenyaw Chan, and Lemuel Moyé Advances on Models, Characterizations and Applications, N. Balakrishnan, I. G. Bairamov, and O. L. Gebizlioglu Survey Sampling: Theory and Methods, Second Edition, Arijit Chaudhuri and Horst Stenger Statistical Design of Experiments with Engineering Applications, Kamel Rekab and Muzaffar Shaikh Quality By Experimental Design, Third Edition, Thomas B. Barker Handbook of Parallel Computing and Statistics, Erricos John Kontoghiorghes Statistical Inference Based on Divergence Measures, Leandro Pardo A Kalman Filter Primer, Randy Eubank © 2006 by Taylor & Francis Group, LLC

Handbook of Parallel Computing and Statistics Edited by Erricos John Kontoghiorghes University of Cyprus and Birkbeck College, University of London, UK © 2006 by Taylor & Francis Group, LLC Boca Raton London New York

DK2384_Discl.fm Page 1 Friday, November 11, 2005 5:42 PM Published in 2006 by Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8247-4067-X (Hardcover) International Standard Book Number-13: 978-0-8247-4067-2 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress Taylor & Francis Group is the Academic Division of Informa plc. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2006 by Taylor & Francis Group, LLC

i i Erricos John Kontoghiorghes: Handbook of Parallel Computing and Statistics DK2384 prelims 2005/11/16 10:12 i i Dedication This book is dedicated to Laurence, Louisa, Ioanna, and Emily © 2006 by Taylor & Francis Group, LLC i i i i

i i Erricos John Kontoghiorghes: Handbook of Parallel Computing and Statistics DK2384 prelims 2005/11/16 10:12 i i Preface Over the last decades a wealth of parallel algorithms has been discovered for solving a wide range of problems that arise in diverse applications areas. Effort has been concentrated mainly on the solution of large scale industrial and engineering problems. Although some of these application areas, such as signal processing and pattern recognition, involve signiﬁcant statistical computing components, the development of parallel algorithms for general use in statistics and econometrics remains comparatively neglected. This is, to some extent, due to a lack of strong interaction between the parallel computing and statistical communities. A number of current parallel numerical libraries provide subroutines that are useful to statisti- cians. For example, most of them offer routines to solve constrained least squares problems and matrix problems that arise in statistical modelling and estimation. However, these routines have been constructed as numerical tools for general use and are unsuitable for the efﬁcient solution of statistical problems that exhibit special properties and characteristics. The design of speciﬁcally targeted parallel numerical libraries and tools to facilitate the solution of computationally inten- sive statistical problems requires close collaboration between statisticians and parallel computing experts [1–3]. The aim of this handbook is twofold: ﬁrst, to provide an overview of the state-of-the-art in par- allel algorithms and processing from a statistical computing standpoint; and, second, to contribute toward the development and deepening of research in the interface between parallel and statistical computation. REFERENCES [1] E.J. Kontoghiorghes. Parallel Algorithms for Linear Models: Numerical Methods and Estima- tion Problems. Advances in Computational Economics, Vol. 15. Kluwer Academic Publishers, Boston, MA, 2000. [2] E.J. Kontoghiorghes. Parallel processing and statistics. Special issue, Computational Statistics & Data Analysis, 31(4), 373–516, 1999. [3] E.J. Kontoghiorghes, A. Nagurney, and B. Rustem. Parallel Computing in economics, ﬁnance, and decision-making. Special issue, Parallel Computing, 26(5), 507–676, 2000. © 2006 by Taylor & Francis Group, LLC i i i i

i i Erricos John Kontoghiorghes: Handbook of Parallel Computing and Statistics DK2384 prelims 2005/11/16 10:12 i i Editor Erricos John Kontoghiorghes received a B.Sc. and Ph.D. from Queen Mary College, University of London, United Kingdom. He is a faculty member of the Department of Public and Business Ad- ministration at University of Cyprus and holds a visiting professorship at Birkbeck College, Univer- sity of London, United Kingdom. Previously, he held faculty positions at City University Business School, London, United Kingdom and University of Neuchatel, Switzerland, and held various visiting appointments at INRIA-IRISA, France. Dr. Kontoghiorghes has published over 50 technical papers in journals and books in the interface research area of parallel computing, statistics, econometrics, and numerical linear algebra. He has authored or edited 7 books, and edited 11 special issues of journals. He is a co-editor of the Journal of Computational Statistics & Data Analysis (Elsevier), editor-in-chief of the Handbook Series of Computing and Statistics with Applications (Elsevier), and a member of the editing committees of various journals. He was elected vice-president of the International Association for Statistical Computing (IASC) in April 2005. © 2006 by Taylor & Francis Group, LLC i i i i

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