# Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms

arXiv: https://arxiv.org/abs/2306.06443 · HTML: https://mlsanity.com/paper/2306.06443/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 10 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model](https://mlsanity.com/paper/1909.01848/) (2019)
- [Semiparametric Estimation with Data Missing Not at Random Using an Instrumental Variable](https://mlsanity.com/paper/1607.03197/) (2016)
- [Semiparametric sensitivity analysis: unmeasured confounding in observational studies](https://mlsanity.com/paper/2104.08300/) (2021)
- [A Versatile Estimation Procedure without Estimating the Nonignorable Missingness Mechanism](https://mlsanity.com/paper/1907.03682/) (2019)
- [On Testability and Goodness of Fit Tests in Missing Data Models](https://mlsanity.com/paper/2203.00132/) (2022)
- [Causal and Counterfactual Views of Missing Data Models](https://mlsanity.com/paper/2210.05558/) (2022)
- [Penalized pairwise pseudo likelihood for variable selection with nonignorable missing data](https://mlsanity.com/paper/1703.06379/) (2017)

## Built on by (most cited first, 4 of 4)

- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)
- [Computational Efficient and Minimax Optimal Nonignorable Matrix Completion](https://mlsanity.com/paper/2504.04016/) (2025)
- [Causal Label Recovery in Payment Networks](https://mlsanity.com/paper/2605.29272/) (2026)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)

## Abstract (arXiv)

Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we consider a MNAR model that generalizes several prior popular MNAR models in two ways: first, it is less restrictive in terms of statistical independence assumptions imposed on the underlying joint data distribution, and second, it allows for all variables in the observed sample to have missing values. This MNAR model corresponds to a so-called criss-cross structure considered in the literature on graphical models of missing data that prevents nonparametric identification of the entire missing data model. Nonetheless, part of the complete-data distribution remains nonparametrically identifiable. By exploiting this fact and considering a rich class of exponential family distributions, we establish sufficient conditions for identification of the complete-data distribution as well as the entire missingness mechanism. We then propose methods for testing the independence restrictions encoded in such models using odds ratio as our parameter of interest. We adopt two semiparametric approaches for estimating the odds ratio parameter and establish the corresponding asymptotic theories: one involves maximizing a conditional likelihood with order statistics and the other uses estimating equations. The utility of our methods is illustrated via simulation studies.