4. Which Resampling-Based Error Estimator for Benchmark Studies? A Power Analysis with Application to PLS-LDA

Resampling-based methods such as k-fold cross-validation or repeated splitting into training and test sets are routinely used in the context of supervised statistical learning to assess the prediction performances of prediction methods using real data sets. In this paper, we consider methodological issues related to comparison studies of prediction methods which involve several real data sets and use resampling-based error estimators as the evaluation criteria. In the literature papers often claim that, say, “Method 1 performs better than Method 2 on real data” without applying any proper statistical inference approach to support their claims and without clearly explaining what they mean by “perform better.” We recently proposed a new statistical testing framework which provides a statistically correct formulation of such paired tests—which are often performed in the machine learning community—to compare the performances of two methods on several real data sets. However, the behavior of the different available resampling-based error estimation procedures in this statistical framework is unknown. In this paper we empirically assess this behavior through an exemplary benchmark study based on 50 microarray data sets and formulate tentative recommendations regarding the choice of resampling-based error estimation procedures in light of the results.