ArticleJournal of the American Statistical Association2020
Ball Covariance: A Generic Measure of Dependence in Banach Space.
Article in Journal of the American Statistical Association, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Identifying genetic variants for brain connectivity using Ball Covariance Ranking and Aggregation.Journal of the American Statistical Association · 2025Article
- Universally Consistent K-Sample Tests via Dependence Measures.Statistics & probability letters · 2025Article
- Conditional Variable Screening for Ultra-High Dimensional Longitudinal Data With Time Interactions.Biometrical journal. Biometrische Zeitschrift · 2024Article
- CRITID: enhancing CRITIC with advanced independence testing for robust multi-criteria decision-making.Scientific reports · 2024Article
- Nonparametric Statistical Inference via Metric Distribution Function in Metric Spaces.Journal of the American Statistical Association · 2024Article
- Statistical Learning Methods for Neuroimaging Data Analysis with Applications.Annual review of biomedical data science · 2023Review
- The Kendall interaction filter for variable interaction screening in high dimensional classification problems.Journal of applied statistics · 2023Article
- Prior Knowledge Guided Ultra-high Dimensional Variable Screening with Application to Neuroimaging Data.Statistica Sinica · 2022Article
- Practical recommendations on double score matching for estimating causal effects.Statistics in medicine · 2022Observational
- A Generic Sure Independence Screening Procedure.Journal of the American Statistical Association · 2019Article
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5 authors.
Funding
Abstract
Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of the existing measures, we propose Ball Covariance as a generic measure of dependence between two random objects in two possibly different Banach spaces. Our Ball Covariance possesses the following attractive properties: (i) It is nonparametric and model-free, which make the proposed measure robust to model mis-specification; (ii) It is nonnegative and equal to zero if and only if two random objects in two separable Banach spaces are independent; (iii) Empirical Ball Covariance is easy to compute and can be used as a test statistic of independence. We present both theoretical and numerical results to reveal the potential power of the Ball Covariance in detecting dependence. Also importantly, we analyze two real datasets to demonstrate the usefulness of Ball Covariance in the complex dependence detection.
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