U-Statistics, Mm-Estimators and Resampling

This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U -statistics and M m -estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.

Introduces a broad class of statistical estimators that are minimizers of convex functions Covers the three important topics in statistics: U-statistics, Mm-estimates and resampling Provides an elementary introduction to resampling in the context of these estimators Presents a quick and short introduction to the statistical software R

Auteur

Arup Bose is Professor at the Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India. He is a Fellow of the Institute of Mathematical Statistics and of all the three national science academies of India. He has significant research contributions in the areas of statistics, probability, economics and econometrics. He is a recipient of the Shanti Swarup Bhatnagar Prize and the C R Rao National Award in Statistics. His current research interests are in large dimensional random matrices, free probability, high dimensional data, and resampling. He has authored three books: Patterned Random Matrices, Large Covariance Autocovariance Matrices (with Monika Bhattacharjee) and (with Koushik Saha), published by Chapman & Hall.

Snigdhansu Chatterjee is Professor at the School of Statistics, University of Minnesota, USA. He is also the Director of the Institute for Research in Statistics and its Applications. His research interests are in resampling methods, high-dimensional and big data statistical methods, small area methods, and application of statistics in climate science, neuroscience and social sciences. He has written over 45 research articles.

Résumé
"The aim of the book under review is to provide statistics graduate students, particularly those who work on nonparametric and semiparametric methods, a concise introduction to the techniques with adequate references for further reading. ... the book under review is a good introduction to U-statistics and resampling methods for graduate students." (Zhongwen Liang, Mathematical Reviews, November, 2019)

Contenu
Chapter 1 . Introduction to U -statistics.- Chapter 2. M -estimators and U -statistics.- Chapter 3 . Introduction to resampling.- Chapter 4 . Resampling U-statistics and M-estimators.- Chapter 5. An Introduction to R.