SMOOTHING SEQUENCES OF DATA BY EXTREME SELECTORS
Tertius de Wet, W. J. Conradie · 2006
Non-linear smoothers based on the extreme selectors have been developed as a class with very powerful properties and ideally suited for application to data having impulsive noise, the type of data that often occur in the engineering and financial fields. Some of their properties make them ideally suited as a basis for teaching students about the art and science of data smoothing. These include inter alia their treatment of blockpulses of particular lengths as either signal or noise, its idempotency properties, which powerfully and visually demonstrate the mathematical concept of idempotence (which is often difficult for students to grasp) and the way that they systematically, measurably and monotonically “peel off” variation until one has a sufficiently smooth result. In this paper we define and discuss members of this class of smoothers and illustrate how their properties make them attractive aids in teaching aspects of nonparametric smoothing as well as aspects of Extreme Value Theory. A Standard and Poor 500 financial data set will be used for illustration purposes.