Introduction to Robust and Quasi-Robust Statistical Methods

The term "robustness" does not lend itself to a clear-cut statistical definition. It seems to have been introduced by G. E. P. Box in 1953 to cover a rather vague concept described in the following way by Kendall and Buckland (1981). Their dictionary states:
Robustness. Many test procedures involving probability levels depend for their exactitude on assumptions concerning the generating mechanism, e. g. that the parent variation is Normal (Gaussian). If the inferences are little affected by departure from those assumptions, e. g. if the significance points of a test vary little if the popUlation departs quite substantially from the Normality the test on the inferences are said to be robust. In a rather more general sense, a statistical procedure is described as robust if it is not very sensitive to departure from the assumptions on which it depends.
This quotation clearly associates robustness with applicability of the various statistical procedures. The two complementary questions met with can be expressed as follows: first, how wide is the field of application of a given statistical procedure or, equivalently, is it robust against some departure from the assumptions? Second, how should we design a statistical procedure to be robust or, in other terms, to remain reliable in spite of possible uncertainty in the available information?