Surrogate space based dimension reduction for nonignorable nonresponse

Semiparametric recovery of central dimension reduction space with nonignorable nonresponse

“…In addition, we also compare our proposed estimators to two competing alternatives, the fusion refined estimators FR 1 and FR 2 , defined and discussed in the Online Supplementary Material. This is the main difference of our work from Deng et al (2022). As well, to demonstrate the robustness of our proposed procedure, we present the results of the corresponding estimators when q(⋅) is misspecified in the semiparametric propensity (3).…”

“…• The development of an intuitive and easy-to-implement SIR estimator for nonignorable missing outcomes and established its asymptotic theory, which in our view is a nontrivial advance over existing results. A distinguishing feature of the proposed method, which differs from that of Deng et al (2022), is that it does not require a validation sample that is often costly to construct.…”

“…In addition, our analysis provides a path to addressing an estimation problem in single and multiple index models, to be discussed in Section 6. Recently, Deng, Yang, and Wang (2022) proposed a similar method based on CSE for regression‐calibration. Their method bears similarity to our dimension reduction‐based imputed method but they did not discuss the FR estimator.…”

“…On the other hand, we clarify the theoretical properties of the FR estimator, and demonstrate its shortcomings via an extensive simulation experiment. As well, unlike the method of Deng et al (2022), our proposed method for estimating $$$ \gamma $$$ requires no validation by way of a second sample. We consider this an important advantage of our method over Deng et al (2022), as obtaining additional validation samples is often a costly endeavour.…”

“…As well, unlike the method of Deng et al (2022), our proposed method for estimating $$$ \gamma $$$ requires no validation by way of a second sample. We consider this an important advantage of our method over Deng et al (2022), as obtaining additional validation samples is often a costly endeavour.…”