A paradox concerning nuisance parameters and projected estimating functions

By Masayuki Henmi, Shinto Eguchi. 2004

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Minimax Weight and Q-Function Learning for Off-Policy Evaluation (2019, background): “While it can be counterintuitive that plug-in MSWL is better than MSWL, it is well understood that plug-in based on MLE with a well specified model for the policy can be viewed as a form of control variates (Henmi and Eguchi, 2004; Hanna et al., 2019).”
Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression (2005, unknown): “A sequence of binary indicators ( 1, . . . , N ) shows which subjects are selected ( i =1) at phase 2 for observation of Xi .”