008 - Estimation based on nearest neighbor matching: from density ratio to average treatment effect

Nearest neighbor (NN) matching is a conceptually natural and practically well-used tool to align data sampled from different groups. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN matching. Their theory, however, requires a crucial assumption that the number of NNs, M, is fixed. We reveal something new out of their study and show that, once allowing M to diverge with the sample size, an intrinsic statistic in their analysis actually constitutes a consistent estimator of the density ratio. Furthermore, we show that through selecting a suitable M, this statistic can attain the minimax lower bound of estimation over a Lipschitz density function class. Consequently, with a diverging M, the NN matching with Abadie and Imbens (2011)'s bias correction provably yields a doubly robust estimator of the average treatment effect and is semiparametrically efficient if the density functions are sufficiently smooth and the outcome model is appropriately specified. It can thus be viewed as a precursor of the recently proposed double machine learning estimators.

graph-based statistics

stochastic geometry

double robustness

double machine learning

propensity score 

Mid-Level

Knowledge

International Conference on Health Policy Statistics 2023