Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation

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.

A Histogram Transform for ProbabilityDensity Function Estimation

The estimation of multivariate probability density functions has traditionally been carried out by mixtures of parametric densities or by kernel density estimators. Here we present a new nonparametric approach to this problem which is based on the integration of several multivariate histograms, computed over affine transformations of the training data. Our proposal belongs to the class of averaged histogram density estimators. The inherent discontinuities of the histograms are smoothed, while their low computational complexity is retained. We provide a formal proof of the convergence to the real probability density function as the number of training samples grows, and we demonstrate the performance of our approach when compared with a set of standard probability density estimators.