Related papers: New multivariate Gini's indices
In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to…
Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a…
Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters…
This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al.…
Ratios of quantiles are often computed for income distributions as rough measures of inequality, and inference for such ratios have recently become available. The special case when the quantiles are symmetrically chosen; that is, when the…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
Originally developed for measuring the heterogeneity of wealth measures, inequality indices are quantitative scores that take values in the unit interval, with the zero score characterizing perfect equality. In this paper, we draw attention…
The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to…
Income and wealth allocation are foundational components of how economies operate. These are complex distributions, and it is hard to get a real sense for their dynamics using simplifications like average or median. One metric that…
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
Distance covariance is a measure of dependence between two random variables that take values in two, in general different, metric spaces, see Sz\'ekely, Rizzo and Bakirov (2007) and Lyons (2013). It is known that the distance covariance,…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
Categorical Gini Correlation (CGC), introduced by Dang et al. (2020), is a novel dependence measure designed to quantify the association between a numerical variable and a categorical variable. It has appealing properties compared to…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
Multivariate data occurs in a wide range of fields, with ever more flexible model specifications being proposed, often within a multivariate generalised linear mixed effects (MGLME) framework. In this article, we describe an extended…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
Rerandomization is a strategy of increasing efficiency as compared to complete randomization. The idea with rerandomization is that of removing allocations with imbalance in the observed covariates and then randomizing within the set of…