# Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model

arXiv: https://arxiv.org/abs/1909.01848 · HTML: https://mlsanity.com/paper/1909.01848/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2019.

## Built on by (most cited first, 12 of 12)

- [On Testability and Goodness of Fit Tests in Missing Data Models](https://mlsanity.com/paper/2203.00132/) (2022)
- [Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms](https://mlsanity.com/paper/2306.06443/) (2023)
- [Robust prediction under missingness shifts](https://mlsanity.com/paper/2406.16484/) (2024)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach](https://mlsanity.com/paper/2311.09015/) (2023)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [Causal Label Recovery in Payment Networks](https://mlsanity.com/paper/2605.29272/) (2026)
- [Partially Specified Causal Simulations](https://mlsanity.com/paper/2309.10514/) (2023)
- [Zero Inflation as a Missing Data Problem: a Proxy-based Approach](https://mlsanity.com/paper/2406.00549/) (2024)
- [Markov Missing Graph: A Graphical Approach for Missing Data Imputation](https://mlsanity.com/paper/2509.03410/) (2025)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)
- [Identifiable Deep Latent Variable Models for MNAR Data](https://mlsanity.com/paper/2603.24771/) (2026)

## Abstract (arXiv)

We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called "no self-censoring" or "itemwise conditionally independent nonresponse," which roughly corresponds to the assumption that no partially-observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously-studied data set of HIV-positive mothers in Botswana.