Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.04313

The Earth Mover's Correlation

Tamás F. Móri·Gábor J. Székely
View original source ↗Read source document ↗Export metadata ↓

Abstract

Since Pearson's correlation was introduced at the end of the 19th century many dependence measures have appeared in the literature. Recently we have suggested four simple axioms for dependence measures of random variables that take values in Hilbert spaces. We showed that distance correlation satisfies all these axioms. We still need a new measure of dependence because existing measures either do not work in general metric spaces (that are not Hilbert spaces) or they do not satisfy our four simple axioms. The earth mover's correlation introduced in this paper applies in general metric spaces and satisfies our four axioms (two of them in a weaker form).

Explore related subjects

math.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tamás F. Móri, Gábor J. Székely. 2020-09-09. The Earth Mover's Correlation. https://arxiv.org/abs/2009.04313

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Topological Periodicity Test (TopPT) via Confidence Bound of Time-Delay Embeddings

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing phase-space dynamics of time-series data, where persistent homology can reveal loops associated with periodicity. However, rigorous statistical uncertainty quantification for these features remains underdeveloped. First, we analyze the topology of time-delay embeddings, showing that the embedded trajectory is homotopy equivalent to a circle ($S^1$) for periodic signals and contractible for non-periodic ones. We also prove a positive lower bound on the embedding reach, ensuring stable topological features. Second, we develop a subsampling approach to construct confidence bounds for persistence diagrams. Under standard manifold regularity conditions, we derive data-dependent bounds with asymptotic guarantees. Finally, we propose Topological Periodicity Test (TopPT), a hypothesis testing framework for periodicity with asymptotically controlled type I and type II error rates. Experiments on bounded-error synthetic data show that raw TDA detects periodic alternatives while avoiding false rejections on structured non-periodic signals, and that the robust rule is conservative after interpolation-error correction. On PhysioNet Fantasia and BIDMC respiratory waveforms, TDA detects most records but only a subset of local windows, unlike scalar periodogram baselines.

math.ST↗
arXiv2026

A note on estimation of quarticity based on spot volatility

We study an estimator of twice the integrated quarticity of a continuous Itô semimartingale, constructed from squared returns and local estimates of spot volatility. For a shrinking estimation window, we establish a functional stable central limit theorem for a bias-corrected version of the estimator. The limiting conditional variance is $56\int_0^t c_s^4\dd s$, where $c$ denotes spot variance. The proof identifies a common martingale approximation for the three components of the estimator and determines their joint covariance structure. The volatility process may have jumps. We also compare the limiting variance with those of the realized-quarticity and quadratic spot-volatility estimators.

math.ST↗
arXiv2026

Revisiting the Brunner-Munzel test from the viewpoint of local linear approximation

The Brunner-Munzel (BM) test is a nonparametric test for two independent samples that evaluates whether observations from one group tend to be greater than observations from another group, or vice versa. The BM test has a broader scope of application than the Mann-Whitney $U$ test because it does not assume equal variances between the two groups. However, the meaning of the BM test statistic is difficult to understand intuitively, which may be one of the factors hindering the widespread use of the BM test. To alleviate this problem, in this paper, I introduce an alternative interpretation of the BM test statistic from the viewpoint of local linear approximation. It is shown that the variance estimator for the sample stochastic superiority used in the BM test can be derived using local linear approximation, in which the influence of each observation on the sample stochastic superiority is assumed to be additive. This simple interpretation will help practitioners decide to use the BM test without hesitation.

math.ST↗