Valid Post-Matching Inference for CRM

Develop fully valid post-matching inference procedures for Centroid-Referenced Mahalanobis Matching that account simultaneously for the learned partition, nonsmooth matching, finite-cell sampling, and possible representation bias.

Background

Centroid-Referenced Mahalanobis Matching currently reports paired-bootstrap intervals as approximate measures of variability. The paper documents sub-nominal empirical coverage and explains that the paired bootstrap does not account for uncertainty induced by learning the partition. Additional complications arise from nonsmooth matching, finite-cell sampling, and residual confounding caused by an inadequate representation. The authors therefore leave unresolved the construction of inference procedures with formal validity after CRM matching.

References

Fully valid post-matching inference for CRM remains a theoretical problem: it must account simultaneously for the learned partition, nonsmooth matching, finite-cell sampling, and possible representation bias.

— Centroid-Referenced Mahalanobis Matching (CRM): A Scalable, Representation-Based Framework for Causal Inference in Large Observational Studies  (2608.18417 - Hu et al., 19 Aug 2026) in Section 5.1, subsection "Uncertainty Quantification"; Appendix B, "Conservative Variance and Bias-Correction Diagnostics"