Estimating the density in a subgroup with imputed subgroup indicators

Abstract

In this paper, I consider the problem of how to estimate the density in a subgroup when some of the subgroupindicatorsaremissingatrandom.Fourdifferentimputationestimatorsarecomparedtoeachotherandtoaninverseprobabilityweightedestimatorsuggestedpreviously.Anoptimalestimatorisderived.I alsoprovideexpressionsfortheasymptoticvarianceoftheimputationestimatorsincludingtermsoforder1 /( nh ) and 1 / n .