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This paper is from Session 3F: Teaching nonparametric methods

which comes under Topic 3: Statistics education at the post-secondary level             Full topic list

(Thursday 6th, 14:00-15:30)

Smoothing sequences of data by extreme selectors

Presenter

• Tertius de Wet (South Africa)

Co-author

• Willie Conradie

Abstract

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.