Testing for Association via Automated Order Selection
The tests in Chapter 6 assumed a fixed smoothing parameter. In Chapters 7 and 8 we will discuss tests based on data-driven smoothing parameters. The current chapter deals with testing the “no-effect” hypothesis, and Chapter 8 treats more general parametric hypotheses. The methodology proposed in Chapter 7 makes use of an orthogonal series representation for r. In principle any series representation could be used, but for now we consider only trigonometric series. This is done for the sake of clarity and to make the ideas less abstract. Section 7.8 discusses the use of other types of orthogonal series.
KeywordsRegression Function Fourier Coefficient Order Selection Piecewise Smooth Function Standard Normal Random Variable
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