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

Autorentext

Arup Bose is an Honorary Visiting Professor at the Indian Statistical Institute since his superannuation in 2024. He has published more than 150 research articles in probability, statistics, econometrics and economics., as well as six books (singly or with others) covering topics in random matrices, non-commutative probability, U-statistics, Mm estimates, resampling, and martingales. He is a Fellow of the Institute of Mathematical Statistics, the Indian National Science Academy, the National Academy of Science and the Indian Academy of Sciences. He has won the Shanti Swarup Bhatnagar Prize and the C.R. Rao award from the Governemtn of India, and the Mahalanobis International Award for Lifetime Achievements from the International Statistical Institute.

Klappentext

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.

Inhalt
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.