Likelihood Ratio Tests and Related Topics in Multivariate Analysis
Description
This book of selected works exhibits a significant part of Carlos A. Coelho's research activity in multivariate statistics, focusing on topics related to likelihood ratio tests. After two introductory chapters, including a biography and an overview of the contributions and related research, the articles are presented in their chronological order of publication, thus also showing the research path followed by the author. The volume shows how likelihood ratio tests useful in multivariate analysis can be developed, and how in most cases exact distributions can be obtained for their statistics in a manageable form. Furthermore, it shows how extremely sharp asymptotic (near-exact) approximations can be found in the remaining cases. Circular distributions are also addressed and, more generally, distributions of products of random variables. The book will be useful for advanced students as well as researchers and practitioners who deal with likelihood ratio tests in multivariate analysis.
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Barry C. Arnold is a Distinguished Professor Emeritus of Statistics at the University of California, Riverside. He is a fellow of the American Statistical Association, the American Association for the Advancement of Science, and of the Institute of Mathematical Statistics and is an Elected Member of the International Statistical Institute. His research interests include order statistics, record values, inequality measurement and ordering, conditionally specified distributions, multivariate models, and income distributions.
Ashis SenGupta is a CSIR (Council of Scientific and Industrial Research) Emeritus Scientist, Ministry of Science and Technology, Government of India, at the Indian Institute of Technology, Kharagpur, India; Adjunct Professor at Augusta University, Georgia, USA; Distinguished Professor at the Middle East Technical University, Turkey; and Advisor/Consultant and former Head and HAG Professor at the Applied Statistics Unit, Indian Statistical Institute, Kolkata, India. He has been a Visiting Professor at several universities worldwide and is the author of over 120 publications, including 14 books and volumes, published by Springer, World Scientific, and Wiley, among others. His research interests include directional statistics, distribution theory, financial statistics, large-scale surveys, multivariate statistical inference, reliability inference, and statistical machine learning. He is an Elected Member of the International Statistical Institute, and a Fellow of the National Academy of Sciences - India, the Indian Society for Probability and Statistics, the International Artificial Intelligence Industry Alliance, and the American Statistical Association.
Gratiela Boca is an Associate Professor at the Department of Economics, Faculty of Sciences, Cluj-Napoca University of Technology, Romania. She is the author of 20 books and over 78 journal articles in the fields of quality management, change management, manufacturing process and quality audit. She is involved in several Erasmus projects with Universities from Turkey, Italy, Finland, Germany and Greece, with a focus on transfer of innovation.
Content
Preface.- Biography of Carlos A. Coelho.- Overview of Carlos A. Coelho's contributions included in the book and related research.- C. A. Coelho: The Generalized Integer Gamma Distribution - a Basis for Distributions in Multivariate Statistics. Journal of Multivariate Analysis.- C. A. Coelho: Addendum to the paper 'The Generalized Integer Gamma Distribution - a Basis for Distributions in Multivariate Analysis'.- C. A. Coelho: The Generalized Near-Integer Gamma distribution - a basis for 'near-exact' approximations to the distributions of statistics which are the product of an odd number of particular independent Beta random variables.- C. A. Coelho: The wrapped Gamma distribution and wrapped sums and linear combinations of independent Gamma and Laplace distributions.- Coelho and J. T. Mexia: On the distribution of the product and ratio of independent generalized Gamma-ratio random variables.- C. A. Coelho and F. J. Marques: The advantage of decomposing elaborate hypotheses on covariance matrices into conditionally independent hypotheses in building near-exact distributions for the test statistics.- C. A. Coelho, B. C. Arnold, and F. J. Marques: Near-exact distributions for certain likelihood ratio test statistics.- F. J. Marques, C. A. Coelho, and B. C. Arnold: A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis.- B. C. Arnold, C. A. Coelho, and F. J. Marques: The distribution of the product of powers of independent Uniform random variables - a simple but useful tool to address and better understand the structure of some distributions.- C. A. Coelho, F. J. Marques, and B. C. Arnold: The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting.- C. A. Coelho and A. Roy: Testing the hypothesis of a doubly exchangeable covariance matrix.- C. A. Coelho: On the Distribution of Linear Combinations of Chi-Square Random Variables.- C. A. Coelho and R. P. Alberto: On the Distribution of the Product of Independent Beta Random Variables - Applications.- C. A. Coelho: Testing equality of mean vectors with block-circular and block compound-symmetric covariance matrices.- C. A. Coelho and J. Pielaszkiewicz: The Likelihood Ratio Test of Equality of Mean Vectors with a Doubly Exchangeable Covariance Matrix.
