A third stage in regression tree growing: Searching for statistical reliability

This paper suggests the introduction of a third stage in regresssion tree growing approach. To this aim, a statistical testing procedure based on the {\it F} statistics, is proposed. In particular, the testing procedure is applied to the CART sequence of pruned subtrees, resulting in a single final tree structured prediction rule, which is statistically reliable and might not coincide with any tree in the sequence itself.