Identification and estimation of statistical functionals using incomplete data

Incomplete data, due to missing observations or interval measurement of variables, usually cause parameters of interest in applications to be unidentified except under untestable and often controversial assumptions. However, it is often possible to identify sharp bounds on parameters without making untestable assumptions about the process through which data become incomplete. The bounds contain all logically possible values of the parameters and can be estimated consistently by replacing the population distribution of the data with the empirical distribution. This is straightforward in some circumstances but computationally burdensome in others. This paper describes the general problem and presents an empirical illustration.