Weighted empirical likelihood inference for dynamical correlations

Abstract

A novel approach is proposed based on the weighted empirical likelihood to construct confidence intervals for dynamical correlation of random functions. The properties of the proposed confidence interval are investigated for random functions with regular or irregular observations. It is shown that the confidence interval using our new approach has a more accurate coverage probability than that using the traditional bootstrap method for random functions with irregular observations. Furthermore, simulation studies demonstrate that the new approach is considerably more efficient in computation than the bootstrap method. The new approach is illustrated with three applications. The first application investigates the dynamical correlation of air pollutants. The second application studies the dynamical correlation of EEG signals in different regions of the brain in response to some stimuli. The third application estimates the dynamical correlation of gene expressions during the activation of T-cells.