Robust Independence Tests with Finite Sample Guarantees for Synchronous Stochastic Linear Systems

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means systems driven by jointly i.i.d. noises. Our method provides bounds type I error probabilities distributionfree, i.e., innovations can have arbitrary distributions. algorithm combines confidence region estimates permutation and general dependence measures, such as Hilbert-Schmidt criterion distance covariance, to detect any nonlinear between systems. We also prove consistency of our hypothesis under mild assumptions demonstrate ideas through example autoregressive