On Invariant Coordinate System (ICS) Functionals

On a Vector-Valued Measure of Multivariate Skewness

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

On Exploring Hidden Structures Behind Cervical Cancer Incidence

Finding new etiological components is of great interest in disease epidemiology. We consider time series version of invariant coordinate selection (tICS) as an exploratory tool in the search of hidden structures in the analysis of population-based registry data. Increasing cancer burden inspired us to consider a case study of age-stratified cervical cancer incidence in Finland between the years 1953 and 2014. The latent components, which we uncover using tICS, show that the etiology of cervical cancer is age dependent. This is in line with recent findings related to the epidemiology of cervical cancer. Furthermore, we are able to explain most of the variation of cervical cancer incidence in different age groups by using only two latent tICS components. The second tICS component, in particular, is interesting since it separates the age groups into three distinct clusters. The factor that separates the three clusters is the median age of menopause occurrence.