MRAM - Multivariate Regression Association Measure

Implementations of an estimator for the multivariate regression association measure (MRAM) proposed in Shih and Chen (2026) <doi:10.1016/j.csda.2025.108288> and its associated variable selection algorithm. The MRAM quantifies the predictability of a random vector Y from a random vector X given a random vector Z. It takes the maximum value 1 if and only if Y is almost surely a measurable function of X and Z, and the minimum value of 0 if Y is conditionally independent of X given Z. The MRAM generalizes the Kendall's tau copula correlation ratio proposed in Shih and Emura (2021) <doi:10.1016/j.jmva.2020.104708> by employing the spatial sign function. The estimator is based on the nearest neighbor method, and the associated variable selection algorithm is adapted from the feature ordering by conditional independence (FOCI) algorithm of Azadkia and Chatterjee (2021) <doi:10.1214/21-AOS2073>. For further details, see the paper Shih and Chen (2026) <doi:10.1016/j.csda.2025.108288>.