Conference Agenda

We study the problem of detecting changes in the marginal distributions of a multivariate time series with a novel CUSUM-type detector statistic based on the (maximum-) sliced-Wasserstein distance. This projection-based approach has two appealing properties. Firstly, unlike the family of Wasserstein distances, it does not suffer from the curse of dimensionality. And secondly, by means of the Kantorovich duality, asymptotic properties of the so-defined detector statistic can be derived from results for (sequential) empirical processes for nonstationary time series. This talk presents new weak limit theorems for sequential empirical processes under the functional dependence measure and their application to the given testing problem. Practical implications, limitations and possible extensions are discussed.

The statistical properties of empirical entropic optimal transport (empirical EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational efficiency. In several applications, it has been realized that in addition to the optimal value, also the EOT plan carries important information. For example, in cell biology, colocalization analysis based on the EOT plan has been introduced as a measure for quantification of spatial proximity of different protein assemblies. Despite recent progress in the analysis of its risk properties, a precise understanding of its statistical fluctuations to make it accessible for inference remains elusive to some extent. We derive asymptotic weak convergence result for a large class of functionals of the EOT plan, in which the colocalization process is included. As an application, we obtain uniform confidence bands for colocalization curves and bootstrap consistency. Our theory is supported by simulation studies and is illustrated by real world data analysis from mitochondrial protein colocalization.