On $L_2$-consistency of nearest neighbor matching
This provides a theoretical foundation for NNM in applications like causal inference and reinforcement learning, though it is incremental as it builds on existing matching methods.
The paper tackles the problem of biased sampling and missing data in statistical estimation by analyzing nearest neighbor matching (NNM), showing that it achieves L2-consistency without requiring smoothness or boundedness assumptions in finite dimensions.
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.