  Biased sampling and missing data complicates statistical problems ranging
from causal inference to reinforcement learning. We often correct for biased
sampling of summary statistics with matching methods and importance weighting.
In this paper, we study nearest neighbor matching (NNM), which makes estimates
of population quantities from biased samples by substituting unobserved
variables with their nearest neighbors in the biased sample. We show that NNM
is $L_2$-consistent in the absence of smoothness and boundedness assumptions in
finite dimensions. We discuss applications of NNM, outline the barriers to
generalizing this work to separable metric spaces, and compare this result to
inverse probability weighting.
