Suppose we have a random sample from a population of interest. For each sampled unit we observe the covariate X, which we assume is discrete with support { x 1 , ... , x K }. For some units, we also observe the variable Y. Let D = 1 if we observe Y, and D = 0 otherwise. We are interested in the population mean of Y, θ = 피[ Y ] = ∑ k=1 K p k μ k , where μ k = 피[Y | X = x k ] and p k = Pr (X = x k ). We assume that Y is missing at random (MAR): Y ⊥ D | X. Suppose also that the propensity score e… CONTINUE READING