  This paper focuses on a data-rich environment where the data set has a very
large cross-sectional dimension, is likely to exhibit local dependence, and yet
is hard to determine the dependence ordering. Such a situation arises, for
example, when the data set is collected from the Internet, through a method of
web crawling. This paper proposes an approach of randomized subsampling
inference, where one constructs a test statistic by aggregating many randomized
test statistics using random draws of subsamples, and uses for inference the
conditional distribution of the test statistic given data. This paper explores
two approaches of such inference: one based on an M-type statistic constructed
from randomized mean statistics and the other based on a U-type statistic
constructed from randomized U-statistics. This paper provides conditions for
local dependence, the number of the random draws, and the subsample size, under
which randomized subsampling inference is asymptotically valid. From the Monte
Carlo simulation studies, this paper finds that the randomized subsampling
inference based on the U-type statistics performs better than that based on the
M-type statistics.
