k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA
研究了用k近邻方法估计未知密度倒数加权函数期望的问题，证明了估计量在严格平稳时间序列数据下的一致性、渐近正态性和半参数有效性，蒙特卡洛实验显示有限样本表现良好。
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 $\root \of 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.