Ordinal pattern dependence as a multivariate dependence measure

In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures. Furthermore, we consider multivariate generalizations of established univariate dependence measures like Kendall's $\tau$, Spearman's $\rho$ and Pearson's correlation coefficient. Among these, only multivariate Kendall's $\tau$ proves to take the dynamical dependence of random vectors stemming from multidimensional time series into account. Consequently, the article focuses on a comparison of ordinal pattern dependence and multivariate Kendall's $\tau$. To this end, limit theorems for multivariate Kendall's $\tau$ are established under the assumption of near epoch dependent, data-generating time series. We analyze how ordinal pattern dependence compares to multivariate Kendall's $\tau$ and Pearson's correlation coefficient on theoretical grounds. Additionally, a simulation study illustrates differences in the kind of dependencies that are revealed by multivariate Kendall's $\tau$ and ordinal pattern dependence

Ordinal Pattern Dependence in the Context of Long-Range Dependence

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings

kk-means clustering of extremes

The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means algorithm can be applied in the analysis of only the extremal observations from a data set. By making use of multivariate extreme value analysis we show how it can be adopted to find "prototypes" of extremal dependence and we derive a consistency result for our suggested estimator. In the special case of max-linear models we show furthermore that our procedure provides an alternative way of statistical inference for this class of models. Finally, we provide data examples which show that our method is able to find relevant patterns in extremal observations and allows us to classify extremal events

Bayesian joint spatio-temporal analysis of multiple diseases

In this paper we propose a Bayesian hierarchical spatio-temporal model for the joint analysis of multiple diseases which includes specific and shared spatial and temporal effects. Dependence on shared terms is controlled by disease-specific weights so that their posterior distribution can be used to identify diseases with similar spatial and temporal patterns. The model proposed here has been used to study three different causes of death (oral cavity, esophagus and stomach cancer) in Spain at the province level. Shared and specific spatial and temporal effects have been estimated and mapped in order to study similarities and differences among these causes. Furthermore, estimates using Markov chain Monte Carlo and the integrated nested Laplace approximation are compared.Peer Reviewe