Estimating the Density in a Subgroup With Imputed Subgroup Indicators

In this paper, I consider the problem of how to estimate the density in a subgroup when some of the subgroup indicators are missing at random. Four different imputation estimators are compared to each other and to an inverse probability weighted estimator suggested previously. An optimal estimator is derived. I also provide expressions for the asymptotic variance of the imputation estimators including terms of order 1/(nh) and 1/n.