A law of large numbers for quadratic forms in near-epoch dependent random fields and its application

摘要

This article establishes a new law of large numbers (LLN) for quadratic forms in near-epoch dependent (NED) random fields where existing LLNs are inapplicable due to unboundedness of pairwise distances between locations. The regularity conditions impose suitable moment and dependence-decay restrictions for NED random fields and their α -mixing bases. Our proposed LLN just requires weighting matrices in the quadratic forms to be uniformly bounded in both row and column sum norms in absolute value, without imposing the localized spatial structure typically required to preserve the NED property after row filtering. As an application, we demonstrate the stochastic convergence of the sample moment functions used in efficient GMM estimation with α -mixing regressors.