Each week, we select a recently published Open Access article to feature. This week’s article comes from the Scandinavian Journal of Statistics and presents a clustering approach that allows for rigorous statistical error control similar to a statistical test.

The article’s abstract is given below, with the full article available to read here.

Vogt, M, Schmid, M. Clustering with statistical error control. Scand J Statist. 2020; 1– 32. https://doi.org/10.1111/sjos.12450

This article presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on a tuning parameter α which is similar to the significance level of a statistical hypothesis test. By choosing α, one can control the probability of overestimating the true number of clusters, while the probability of underestimation is asymptotically negligible. In addition, the probability that the estimated clusters differ from the true ones is controlled. In the theoretical part of the article, formal versions of these statements on statistical error control are derived in a baseline model with convex clusters. A simulation study and two applications to temperature and gene expression microarray data complement the theoretical analysis.