Related papers: An Interpretable Measure for Quantifying Predictiv…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
In contingency table analysis, the odds ratio is a commonly applied measure used to summarize the degree of association between two categorical variables, say R and S. Suppose now that for each individual in the table, a vector of…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…
We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most…
In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…
Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby relations may be coarsened and refined according…
Nonignorable missing data, where the probability of missingness depends on unobserved values, presents a significant challenge in statistical analysis. Traditional methods often rely on strong parametric assumptions that are difficult to…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in…
Reliability sensitivity analysis is concerned with measuring the influence of a system's uncertain input parameters on its probability of failure. Statistically dependent inputs present a challenge in both computing and interpreting these…