NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA
针对按家庭汇总的数据，提出一种核估计量来估计密度函数和回归函数，允许家庭内存在共同成分但家庭间独立，证明了估计量的一致性和渐近正态性，并通过蒙特卡洛实验考察了实际表现。
We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.