The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

APPENDIX F

Robust Statistics

Robust statistics addresses the problem of making estimates that are insensitive 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 information 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 nonlinearity. 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) creates new estimates that are insensitive to small changes in some of the assumptions. 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 ...