Robust Statistics, 2nd Edition

2Location and Scale

2.1 The location model

For a systematic treatment of the situations considered in Chapter 1, we need to represent them by probability‐based statistical models. We assume that the outcome of each observation depends on the “true value” of the unknown parameter (in Example 1.1, the copper content of the whole flour batch) and also on some random error process. The simplest assumption is that the error acts additively:

2.1

where the errors are random variables. This is called the location model.

If the observations are independent replications of the same experiment under equal conditions, it may be assumed that

• have the same distribution function
• are independent.

It follows that are independent, with common distribution function

2.2

and we say that the are i.i.d ...