Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

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Likelihood-Based Inference on Haplotype Effects in Genetic Association Studies (2006, methodology): “3) of Breslow et al. The key difference is that the former involves several nonparametric components {Fg(·)}, whereas the latter involves only a single nonparametric function. Despite this difference, the arguments of Breslow et al. can be used to prove Theorem 1 with minor modifications. Specifical”
Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression (2005, unknown): “The efficiency loss has been determined for parametric regression models fitted to two-phase stratified data, where numerical evaluation of profile likelihoods and explicit calculation of information bounds are both feasible (Lawless et al., 1999; Breslow et al., 2003).”
Semiparametric efficiency in GMM models with auxiliary data (2007, unknown): “We provide new results on semiparametric efficiency bounds for the “verify-out-of-sample” case.”