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Erschienen in:
2017 | OriginalPaper | Buchkapitel
5. DD Plots and Prediction Regions
verfasst von : David J. Olive
Erschienen in: Robust Multivariate Analysis
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Abstract
This chapter examines the DD plot of classical versus robust Mahalanobis distances and develops practical prediction regions for a future test observation \(\varvec{x}_f\) that work even if the iid training data \(\varvec{x}_1, ..., \varvec{x}_n\) come from an unknown distribution. The prediction regions can be visualized with the DD plot. The classical prediction region assumes that the data are iid from a multivariate normal distribution, and the region tends to have too small of a volume if the MVN assumption is violated. The undercoverage of the volume of the classical region becomes worse as the number of variables p increases since the volume of the region \(\{ \varvec{x}: D_{\varvec{x}}(\overline{\varvec{x}},{\varvec{S}}) \le h \} \propto h^p\). The classical region uses \(h_c = \sqrt{\chi ^2_{p, 1-\delta }}\), which tends to be much smaller than the value of h that gives correct coverage.