Best Linear Predictor with Missing Response: Locally Robust Approach
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This paper provides asymptotic theory for Inverse Probability Weighing (IPW) and Locally Robust Estimator (LRE) of Best Linear Predictor where the response missing at random (MAR), but not completely at random (MCAR). We relax previous assumptions in the literature about the first-step nonparametric components, requiring only their mean square convergence. This relaxation allows to use a wider class of machine leaning methods for the first-step, such as lasso. For a generic first-step, IPW incurs a first-order bias unless the model it approximates is truly linear in the predictors. In contrast, LRE remains first-order unbiased provided one can estimate the conditional expectation of the response with sufficient accuracy. An additional novelty is allowing the dimension of Best Linear Predictor to grow with sample size. These relaxations are important for estimation of best linear predictor of teacher-specific and hospital-specific effects with large number of individuals.
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