This paper focuses on a situation where data exhibit local dependence but their dependence ordering is not known to the econometrician. Such a situation arises, for example, when many differentiated products are correlated locally and yet the correlation structure is not known, or when there are peer effects among students' actions but precise information about their reference groups or friendship networks is absent. This paper introduces an ordering-free local dependence measure which is invariant to any permutation of the observations, and can be used to express various notions of temporal and spatial weak dependence. The paper begins with the two-sided testing problem of a population mean, and introduces a randomized subsampling approach where one performs inference using U-statistic type (or V-statistic type) test statistics that are constructed from randomized subsamples. The paper shows that one can obtain inference whose validity does not require knowledge of dependence ordering, as long as local dependence is sufficiently "local" in terms of the ordering-free local dependence measure. The method is extended to models defined by moment restrictions. This paper provides results from Monte Carlo studies.
The paper is written with an econometrics journal in mind, but it is fundamentally concerned with a statistics problem.