Statistical Inference Based on the Density Power Divergence: The Robustness Perspective

All scientists, researchers and data analysts, who handle real data as part of their scientific explorations, have, from time to time, to face to the problem of having to deal with data which do not exactly conform to the model which was expected to describe these data. Often such non-conformity is manifested through outliers. Classical techniques, which are usually optimal for "pure" data, generally have poor resistance to "noisy" data consisting of outliers or exhibiting other forms of model misspecification. This manuscript discusses a particular method of inference which employs a robust minimum distance approach for noisy data.

• Provides all the up-to-date details about a very popular robust inference method based on the density power divergence within one cover

• Covers the general theory as well as applications to special types of data like survival data, count data, binary data, time series data, extreme value data and many more

• Discusses the extreme value problem from the robustness perspective

• Guides the readers for practical use of this popular robust inference method through several real life examples along with their implementation in the statistical software R.

• Contains many open problems in this popular research area of robust inferences which will help the readers to choose their new research problems and enrich the field by solving them

This book is aimed primarily at advanced graduate students, research scholars and scientist working on robust statistical methods. Researchers from several applied fields (like biology, economics, medical sciences, sociology, business & finance etc.) who need to analyse their experimental data with some potential noises and outliers will also find this book useful.

Ayanendranath Basu got his PhD in Statistics from the Pennsylvania State University, USA, in 1991, working under the supervision of Professor Bruce G. Lindsay. After graduation he spent four years at the Department of Mathematics, University of Texas at Austin, USA, as an Assistant Professor. He returned to India and joined the Indian Statistical Institute in 1995, where he is currently a Higher Academic Grade (HAG) Professor at the Interdisciplinary Statistical Research Unit. The primary focus of his research work is on robust statistics and statistical inference based on divergence measures. He was written about 110 refereed journal articles in reputed international journals which include Biometrika, Journal of the American Statistical Association, Bernoulli, Statistica Sinica, Electronic Journal of Statistics, IEEE Transactions in Information Theory and many others. He has authored two books (both from CRC Press) and edited several others. He has supervised the PhD thesis of five students, and is currently supervising several more. He is a recipient of the C. R. Rao National Prize in Statistics of Government of India. He is a fellow the National Academy of Sciences, India, and the West Bengal Academy of Science and Technology.

Abhik Ghosh is currently an Assistant professor in the Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata. He received his B.Stat. (Honours) and M.Stat. (Specialization: Mathematical Statistics and Probability) degrees with gold medals in 2010 and 2012, respectively, from the Indian Statistical Institute (ISI), Kolkata, India. He then completed his PhD in Statistics from the same institute in 2015 under the guidance of Prof. Ayanendranath Basu and did his postdoctoral research at the University of Oslo, Norway. His research involves divergence measures and minimum divergence inference, data robustness under the Bayesian paradigm, robust and high-dimensional statistical methods with applications to biostatistics and biometrics, robust testing of hypothesis, etc. He has received several international recognitions for his research. These include the first place at the Jan Tinbergen Awards (2013) for young statisticians from developing countries given by the International Statistical Institute, 2017 ISCB Conference Award for Scientists from International Society of Clinical Biostatistics (ISCB), an IMS New Researcher Travel Award given by Institute of Mathematical Statistics (IMS), and an IBS Travel Award from the International Biometric Society (IBS). He has also received the 2016 ISCA Young Scientist Award in Mathematical Sciences from Indian Science Congress Association (ISCA), the 2016 Prof. A. M. Mathai Award from the Indian Mathematical Society, the 2017 Bose-Nandi Young Statistician Award (1st Place) given by the Calcutta Statistical Association (CSA), and many more national award.

Leandro Pardo got his PhD from the Complutense University of Madrid, Spain, in 1980, where he is currently a Full Professor. He does research in many areas of statistics and probability, but his primary interest is in statistical inference based on divergence measures. He has published extensively and has more than 250 papers in refereed international journals. He has written a major research monograph on divergence measures (published by Chapman and Hall/CRC). He has guided eight PhD dissertations and continues to guide more students. He is a past president of the Spanish Society of Statistics and Operations Research. He has also contributed significantly to editorial work, and, among other activities, is a former Editor-in-Chief of TEST. He is also an elected member of the International Statistical Institute. He has also had a large number of funded research projects during his long career.