Statistical Analysis with Missing Data., 3rd Edition

12Models for Robust Estimation

12.1 Introduction

A feature of the model-based approach to statistics in general is that it makes explicit assumptions about the distribution of the data. Some view this as a negative, arguing that all models are wrong,¹ so inference based on models is always flawed. On the other hand, other approaches to inference, such as methods based on generalized estimating equations, often have implicit assumptions that are rarely subject to scrutiny. Making assumptions explicit lays them open to criticism, and criticism can lead to fixing doubtful assumptions and generating better inferences.

Robust estimation, and more generally robust inference, concerns methods that do not rely on strong assumptions about the structure of the model or the form of the error distribution. The early literature (see for example Andrews et al. 1972; Hampel et al. 1986) focused mainly on methods for estimating the center of a symmetric distribution that are resistant to outliers. This literature was not primarily model-based, but models can be formulated that also yield inferences that are resistant to outliers. These models generally replace the normal distribution for modeling continuous data by a longer-tailed distribution like the t-distribution, or skewed extensions of these distributions. In particular, Examples 8.4, 8.8–8.10, and 10.4 concerned robust inference from a single sample based on the t-distribution, with degrees of freedom fixed a priori or estimated from ...