2016/03/02 by Paul K. Rubenstein, Rubenstein, Paul K., Kacper Chwialkowski +4 · 1 citation
Mathematics · #62G10 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #msc:62G10 #stat.ML
paper · pdf · doi:10.48550/arxiv.1603.00929
15 pages including 5 pages of supplementary material, 3 figures
openalex publication_date 2016/03/02 · arxiv created 2016/03/08 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply a wild bootstrap method to the Lancaster three-variable interaction measure in order to detect factorisation of the joint distribution on three variables forming a stationary random process, for which the existing permutation bootstrap method fails. As in the i.i.d. case, the Lancaster test is found to outperform existing tests in cases for which two independent variables individually have a weak influence on a third, but that when considered jointly the influence is strong. The main contributions of this paper are twofold: first, we prove that the Lancaster statistic satisfies the conditions required to estimate the quantiles of the null distribution using the wild bootstrap; second, the manner in which this is proved is novel, simpler than existing methods, and can further be applied to other statistics.