Directional and Multivariate Statistics

Somesh Kumar is Professor in the Department of Mathematics, Indian Institute of Technology (IIT) Kharagpur, India. He did his M.Sc. in statistics followed by Ph.D. at the IIT Kanpur, respectively, in 1984 and 1990. Before joining the IIT Kharagpur in 1994, he taught at the University of Jammu, India, for five-and-a-half years. He has published more than 130 research papers in refereed international journals and book chapters and supervised 15 Ph.D. scholars. His major research interests are in statistical decision theory and inference, in particular on estimation after selection, quantile estimation, estimation of parameters under constraints, two-stage and sequential estimation, problem of classification, inference on directional distributions, limit theorems for dependent models, estimating measures of reliability and entropy, stochastic ordering and bootstrap tests. His research has found applications in diverse fields like agriculture, medical, mechanical, electronic, environmental and ecological studies. Barry C. Arnold is distinguished Professor Emeritus in the Department of Statistics, University of California, Riverside, USA. He received his Ph.D. in statistics from Stanford University, USA, in 1965. Author of 14 books and more than 275 research papers in reputed peer-reviewed journals and contributed volumes, he has guided 17 Ph.D. scholars and has been on the editorial boards of several journals. His research interests include estimation theory, probability, stochastic processes, mathematical learning models, biological models, characterizations, income distributions, order statistics, inequality measurement, record values, conditionally specified distributions and Bayesian inference. Kunio Shimizu is Project Professor in the Center for Training Professors in Statistics at The Institute of Statistical Mathematics, Tokyo, Japan. He is also Professor Emeritus in the Faculty of Science and Technology at Keio University, Yokohama, Japan. He has worked extensively in the field of directional distributions, modeling of distributions, classification problems and multivariate methods. In 2001, he was awarded the Jacob Wolfowitz prize by the American Journal of Mathematical and Management Sciences, and in 2017, JSS prize of the Japan Statistical Society. Arnab Kumar Laha is Professor of Production and Quantitative Methods at the Indian Institute of Management Ahmedabad, Gujarat. He takes a keen interest in understanding how analytics, machine learning and artificial intelligence can be leveraged to solve complex problems in business and society. He has published his research in national and international journals of repute, authored a popular book on analytics, and an edited book volume published by Springer. He was named one of the “20 Most Prominent Analytics and Data Science Academicians in India” by the Analytics India Magazine, in 2018.

• Chapter 1 Circular Data Diagnostics in Regression and Time Series Models.- Chapter 2 The Weighting Approach on the Circle.- Chapter 3 Isotonic Regression Estimators for Simultaneous Estimation of Order Restricted Location/Scale Parameters of a Bivariate Distribution: A Unified Study.