Reliability Measures for Local Nodes Assessment in Classification Trees

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Abstract
Most of the modern developments with classification trees are aimed at improving their predictive capacity.This article considers a curiously neglected aspect of classification trees, namely the reliability of predictions that come from a given classification tree. In the sense that a node of a tree represents a point in the predictor space in the limit, the aim of this article is the development of localized assessment of the reliability of prediction rules. A classification tree may be used either to provide a probability forecast, where for each node the membership probabilities for each class constitutes the prediction, or a true classification where each new observation is predictively assigned to a unique class. Correspondingly, two types of reliability measure will be derived—namely, prediction reliability and classification reliability. We use bootstrapping methods as the main tool to construct these measures. We also provide a suite of graphical displays by which they may be easily appreciated. I...

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