Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and Ph D students. Happy Birthday, C.R. Rao!
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Preface.- Dedication.- Part I – Inference.- Robust Statistical Inference for One-shot Devices Based on Density Power Divergences: An Overview (N. Balakrishnan, E. Castilla, L. Pardo).- Statistical Meaning of Mean Functions: A Novel Matrix Mean Derived from Fisher Information, authors: A.M. Kagan, P.J. Smith).- The Legend of the Equality of OLSE and BLUE: highlighted by C.R. Rao in 1967 (A. Markiewicz, S. Puntanen, G.P.H. Styan).- Comparison of Local Powers of Some Exact Tests for a Common Normal Mean with Unequal Variances (Y.G. Kifle, A.M. Moluh, B.K. Sinha).- Quantile Function: Overview of Collaboration with Professor C. R. Rao (G.J. Babu).- Part II – Distribution Theory.- Some Bivariate and Multivariate Models Involving Independent Gamma Distributed Components (B.C. Arnold).- An Absolute Continuous Bivariate Inverse Generalized Exponential Distribution: Properties, Inference and Extensions (D. Kundu).- Part III – Multivariate Analysis.- The Likelihood Ratio Test of Equality of Mean Vectors with a Doubly Exchangeable Covariance Matrix (C.A. Coelho, J. Pielaszkiewicz).- Bilinear Regression with Rank Restrictions on the Mean and the Dispersion Matrix (D. von Rosen).- Limiting Canonical Distribution of Two Large Dimensional Random Vectors (Z. Bai, Z. Hou, J. Hu, D. Jiang, X. Zhang).- Some Contributions to Multivariate Analysis due to C. R. Rao and Associated Developments (Y. Fujikoshi).- On Testing Structures of the Covariance Matrix: A Non-normal Approach (T. Kollo, M. Valge).- Part IV – Design and Sampling.- The Existence of Perpendicular Multi-arrays (K. Matsubara, S. Kageyama).- Statistical Design Issues for f MRI Studies: A Beginner’s Training Manual (B.K. Sinha, N.K. Mandal, M. Pal).- A Review of Rigorous Randomized Response Methods for Protecting Respondent’s Privacy and Data Confidentiality (T. Nayak).- Part V – Shape and Circular Analysis.- A Statistical Analysis of the Cardioid Radial Growth Model (J.T. Kent, K.V. Mardia, L. Ippoliti, P. Valentini).- A Flexible Family of Mixed Distributions for Discrete Linear and Continuous Circular Random Variables (A. Sen Gupta, K. Shimizu, S.H. Ong, R. Das).- Goodness of Fit for Wrapped Stable Distributions Based on the Characteristic Function (S.G. Meintanis, S.R. Jammalamadaka, Q. Jin).- Part VI – Applications.- Partial Differential Equations Models and Riemann-Stieltjes Integrals in Measuring Sustainability (A.S.R.S. Rao, S. Saride).- Extreme Point Methodology in Power Calculations – The Case of Hardy-Weinberg Equilibrium (S. Venkatesan, M.B. Rao, H.-I. Hsiao).- Part VII – General.- On the Association of Professor C. R. Rao with the Poznan School of Mathematical Statistics and Biometry (T.Calinski).
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Barry C. Arnold is a Distinguished Professor of Statistics at the University of California, Riverside, USA. 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.Narayanaswamy Balakrishnan is a Distinguished University Professor at Mc Master University, Hamilton, Canada. He is a Fellow of the American Statistical Association, Fellow of the Institute of Mathematical Statistics and an Elected Member of the International Statistical Institute. His research interests include ordered data analysis, censoring methodology, univariate and multivariate distribution theory, reliability theory, and survival analysis. He has recently been awarded an Honorary Doctorate by The National University of Athens, Greece.
Carlos A. Coelho is a Full Professor of Statistics at NOVA University of Lisbon, Portugal. He holds a Ph.D. in Biostatistics from the University of Michigan and his main research focuses on developing likelihood ratio tests in multivariate analysis and obtaining their exact distributions in closed finite form, whenever possible, or developing the so-called near-exact distributions for the other cases, which are sharp asymptotic distributions that are asymptotic for all parameters involved.
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