GENERIC UNIFORM-CONVERGENCE AND EQUICONTINUITY CONCEPTS FOR RANDOM FUNCTIONS - AN EXPLORATION OF THE BASIC STRUCTURE

Equicontinuity-type concepts for random functions, which are important for establishing convergence results for such functions, have increas ingly been used in the econometrics literature. In this paper we defin e and discuss various equicontinuity-type concepts for random function s and employ those concepts to provide sufficient conditions for unifo rm convergence and, in particular, for uniform laws of large numbers. Furthermore, we clarify the differences and similarities between unifo rm laws of large numbers based on pointwise and local laws of large nu mbers given in the recent literature as they relate to differences in the employed equicontinuity-type concepts.