Independence test via mutual information in the presence of measurement errors

Among existing methods for independence test, mutual information (MI) has great popularity as it is invariant to monotone transformations and enjoys higher power in detecting nonlinear associations. In this paper, we propose a novel MI-based independence test in the presence of measurement errors. The conditional density functions involved in MI are estimated using a novel deconvolution double kernel method. The convergence rates of these estimates are derived under the assumption that the measurement errors are either ordinary or super smooth. In addition, the asymptotic behaviors of the resultant estimate of MI are established under both the null and alternative hypotheses. Extensive simulation studies and an application to the low-resolution observations of source stars dataset confirm the superior numerical performances of the proposed methods.