U-Statistics, Mm-Estimators and Resampling

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction to U-statistics

   Arup Bose, Snigdhansu Chatterjee

   Abstract

   U statistics are a large and important class of statistics. Indeed, any U-statistic (with finite variance) is the non-parametric minimum variance estimator of its expectation \( \theta \). Many common statistics and estimators are either U-statistics or approximately so.

3. Chapter 2. Mm-estimators and U-statistics

   Arup Bose, Snigdhansu Chatterjee

   Abstract

   M-estimators, and their general versions Mm-estimators, were introduced by Huber (1964) out of robustness considerations. The literature on these estimators is very rich and the asymptotic properties of these estimates have been treated under different sets of conditions. To establish the most general results for these estimators require very sophisticated treatment using techniques from the theory of empirical processes.

4. Chapter 3. Introduction to resampling

   Arup Bose, Snigdhansu Chatterjee

   Abstract

   In the previous two chapters we have seen many examples of statistical parameters and their estimates. In general suppose there is a parameter of interest \( \theta \) and observable data Y = (Y1, . . . , Yn). The steps for statistical inference can be divided into three broad issues.

5. Chapter 4. Resampling U-statistics and M-estimators

   Arup Bose, Snigdhansu Chatterjee

   Abstract

   Recall from Chapter 1 that if Y₁, . . . , Y_n is an i.i.d. sample from some probability distribution function , and \( \theta \) = h(Y₁, Y₂, . . . , Y_m) where h(·) is symmetric in its arguments, then the U-statistic,

6. Chapter 5. An Introduction to R

   Arup Bose, Snigdhansu Chatterjee

   Abstract

   This chapter is a soft introduction to the statistical software called R. We will discuss how to conduct elementary data analysis, use built-in programs and packages, write and run one’s own programs, in the context of the topics covered in this book. All softwares have some specific advantages and several deficiencies, and R is no exception.

7. Backmatter