Weak consistency of the 1-nearest neighbor measure with applications to missing data. (arXiv:1902.02408v3 [math.ST] UPDATED)

When data is partially missing at random, imputation and importance weighting
are often used to estimate moments of the unobserved population. In this paper,
we study 1-nearest neighbor (1NN) importance weighting, which estimates moments
by replacing missing data with the complete data that is the nearest neighbor
in the non-missing covariate space. We define an empirical measure, the 1NN
measure, and show that it is weakly consistent for the measure of the missing
data. The main idea behind this result …

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