Related papers: Ordinal pattern dependence as a multivariate depen…
Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendall's {\tau} coefficient is often used to study the trend of statistics related to the…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
A margin-free measure of bivariate association generalizing Spearman's rho to the case of non-monotonic dependence is defined in terms of two square integrable functions on the unit interval. Properties of generalized Spearman correlation…
For a bivariate time series $((X_i,Y_i))_{i=1,...,n}$ we want to detect whether the correlation between $X_i$ and $Y_i$ stays constant for all $i = 1,...,n$. We propose a nonparametric change-point test statistic based on Kendall's tau and…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. This research goes one step further and considers the transcripts being…
We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…
This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized…
Ordinal measurements are common outcomes in studies within psychology, as well as in the social and behavioral sciences. Choosing an appropriate regression model for analysing such data poses a difficult task. This paper aims to facilitate…
Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are…
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…