405Appendix
FRobust Statistics
R
obust statistics addresses the problem of making estimates that are insen-
sitive to small changes in the basic assumptions of the statistical models
employed. In this appendix we discuss the general concepts and methods of
robust statistics. The reason for doing so is to provide background informa-
tion for the discussion of robust estimation covered in Chapter 8.
Robust Statistics Defined
Statistical models are based on a set of assumptions; the most important include
(1) the distribution of key variables, for example, the normal distribution of
errors, and (2) the model specification, for example, model linearity or nonlin-
earity. Some of these assumptions are critical to the estimation process: if they
are violated, the estimates become unreliable. Robust statistics (1) assesses the
changes in estimates due to small changes in the basic assumptions and (2) cre-
ates new estimates that are insensitive to small changes in some of the assump-
tions. The focus of our exposition is to make estimates robust to small changes
in the distribution of errors and, in particular, to the presence of outliers.
Robust statistics is also useful to separate the contribution of the tails
from the contribution of the body of the data. We can say that robust statistics
and classical nonrobust statistics are complementary. By conducting a robust
analysis, one can better articulate important financial econometric findings.
As observed by Peter Huber, robust, distribution-free, and nonparamet-
rical seem to be closely related properties but actually are not.^1 For example,
the sample mean and the sample median are nonparametric estimates of the
mean and the median but the mean is not robust to outliers. In fact, changes
(^1) Huber’s book is a standard reference on robust statistics: Peter J. Huber, Robust
Statistics (New York: John Wiley & Sons, 1981). See also R. A. Maronna, R. D.
Martin, and V. J. Yohai, Robust Statistics: Theory and Methods (Hoboken, NJ: John
Wiley & Sons, 2006).