Generalized martingale difference divergence: Detecting conditional mean independence with applications in variable screening

Martingale difference divergence measures the departure of conditional mean independence of two random vectors. Generalized martingale difference divergence and its correlation are developed based on symmetric Lévy measures to detect such an independence. Then the proposed generalized martingale difference correlation is utilized as a marginal utility to do high-dimensional variable screening. Both simulation results and real data illustrations show the promising performance of the developed indexes.