Characteristics of multivariate distributions and the invariant coordinate system

A review of second-order blind identification methods

Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed. This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Data.

Cumulants of Multivariate Symmetric and Skew Symmetric Distributions

This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-distribution and related skew-t distribution are discussed in some detail.

Sampling Properties of color Independent Component Analysis

Independent Component Analysis (ICA) offers an effective data-driven approach for blind source extraction encountered in many signal and image processing problems. Although many ICA methods have been developed, they have received relatively little attention in the statistics literature, especially in terms of rigorous theoretical investigation for statistical inference. The current paper aims at narrowing this gap and investigates the statistical sampling properties of the colorICA (cICA) method. The cICA incorporates the correlation structure within sources through parametric time series models in the frequency domain and outperforms several existing ICA alternatives numerically. We establish the consistency and asymptotic normality of the cICA estimates, which then enables statistical inference based on the estimates. These asymptotic properties are further validated using simulation studies.

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.