Optimal Nonparametric Testing Of Missing Completely At Random, And Its Connections To Compatibility

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" summary

Characterises exactly which non‑MCAR alternatives are detectable and reduces detection to a compatibility problem tied to Fréchet classes, then builds a practical test by plugging empirical marginals into a linear programming formulation and computing an incompatibility index. Tests control type‑I error, give explicit Calpha+Cbeta power separations, are consistent against all detectable alternatives, and match minimax separation rates (up to logs) in key discrete cases (canonical 3 bivariate marginals). Code ships on CRAN and a Monte‑Carlo/bootstrap variant improves finite‑sample power.

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" chapters (16)

1. 0:00Introduction
2. 1:07Why Care About Missing Data
3. 3:35Missingness Mechanism
4. 5:24Setting
5. 7:30Existing Work
6. 9:08Consistency
7. 12:12Compatibility
8. 16:57Testing Compatibility
9. 24:27Incompatibility Index
10. 27:20Geometry
11. 28:57Improving Tests
12. 31:09Improved Critical Value
13. 33:07Lower Bounds
14. 34:14Minimax Testing
15. 36:13More Complex Problems
16. 37:42Numerical Results