This paper considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the k-nearest neighbor (k-NN) method. It establishes the √T -consistency and the asymptotic normality of an estimator that allows for strictly stationary time-series data. The consistency of the Bartlett estimator of the derived asymptotic variance is also established. The proposed estimator is also shown to be asymptotically semiparametric efficient in the independent random sampling scheme. Monte Carlo experiments show that the proposed estimator performs well in finite sample applications.

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Journal Econometric Theory
Chu, B, & Jacho-Chávez, D.T. (David T.). (2012). K-nearest neighbor estimation of inverse-density-weighted expectations with dependent data. Econometric Theory, 28(4), 769–803. doi:10.1017/S026646661100079X