2016/03/10 by Ruth Heller, Heller, Ruth, Yair Heller +1 · 1 citation
Agricultural and Biological Sciences · Mathematics · #Advanced Statistical Methods and Models #Econometrics #FOS: Computer and information sciences #FOS: Mathematics #Independence (probability theory) #Mathematics #Methodology (stat.ME) #Multivariate analysis #Multivariate normal distribution #Multivariate random variable #Multivariate statistics #Pesticide Residue Analysis and Safety #Random variable #Statistical Methods in Clinical Trials #Statistics #Statistics Theory (math.ST) #Univariate #Univariate distribution #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1603.03418
arxiv created 2016/03/10 · openalex publication_date 2016/03/10 · arxiv updated 2016/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we provide conditions under which it is enough to have a consistent univariate test of independence on the distances to guarantee that the power to detect dependence between the random vectors increases to one, as the sample size increases. These conditions turn out to be minimal. If the univariate test is distribution-free, the multivariate test will also be distribution-free. If we consider multiple center points and aggregate the center-specific univariate tests, the power may be further improved, and the resulting multivariate test may be distribution-free for specific aggregation methods (if the univariate test is distribution-free). We show that several multivariate tests recently proposed in the literature can be viewed as instances of this general approach.