Robust Statistics, 2nd Edition

1Introduction

1.1 Classical and robust approaches to statistics

This introductory chapter is an informal overview of the main issues to be treated in detail in the rest of the book. Its main aim is to present a collection of examples that illustrate the following facts:

• Data collected in a broad range of applications frequently contain one or more atypical observations, known as outliers; that is, observations that are well‐separated from the majority or “bulk” of the data, or in some way deviate from the general pattern of the data.
• Classical estimates, such as the sample mean, the sample variance, sample covariances and correlations, or the least‐squares fit of a regression model, can be adversely influenced by outliers, even by a single one, and therefore often fail to provide good fits to the bulk of the data.
• There exist robust parameter estimates that provide a good fit to the bulk of the data when the data contains outliers, as well as when the data is free of them. A direct benefit of a good fit to the bulk of data is the reliable detection of outliers, particularly in the case of multivariate data.

In Chapter 3 we shall provide some formal probability‐based concepts and definitions of robust statistics. Meanwhile, it is important to be aware of the following performance distinctions between classical and robust statistics at the outset. Classical statistical inference quantities such as confidence intervals, ‐statistics and ‐values, values and model selection criteria ...