Title: Clustering with Statistical Error Control,
Abstract: This paper 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 alpha which is similar to the
significance level of a statistical hypothesis test. By choosing alpha, 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 paper, formal versions of these
statements on statistical error control are derived in a standard model setting
with convex clusters. A simulation study and two applications to temperature
and gene expression microarray data complement the theoretical analysis.