Relative coarsening at random

Many types of data are often incompletely observed. How incompletely is typically randomly determined. Heitjan and Rubin (Annals of Statistics, 1991) proposed a condition, “coarsened at random” or CAR, ensuring ignorability of this randomness in discrete sample spaces. In general sample spaces CAR comes in two flavors according to whether it is defined in terms of probabilities or densities. In this paper, CAR defined in terms of densities, called relative CAR, is discussed as a condition for ignorability in a statistical model allowing for partial observation of random elements determining the degree of incompleteness in the observation of the data.