Finite-sample optimality of adaptive mid-summary procedures

Establish finite-sample optimality, and extend the strategy to more general densities, for adaptive procedures that integrate sample mid-summaries using data-dependent weights.

Background

Sample mid-summaries and their linear combinations are classical L-estimators for location estimation. Earlier procedures select a single mid-summary or a fixed combination for specified density families, while later work considers data-dependent weighting when the underlying density is unknown.

The cited adaptive mid-summary procedures achieve optimal asymptotic variance for regular location families with finite Fisher information. The paper identifies as unresolved whether such methods can be shown to be optimal in finite samples and whether their approach applies beyond regular families to more general density classes, including distributions with nonstandard or boundary-driven rates.

References

The adaptive mid-summary-based procedure therein can achieve optimal asymptotic variance for regular location families with finite Fisher information, whereas finite-sample optimality and the strategy for more general densities have not yet been established.

— Instance-Optimal Adaptive Location Estimation via Multiscale Mid-Summaries  (2609.20749 - Wang et al., 17 Sep 2026) in Section 1, subsection “Related Work,” paragraph “Location estimation with sample mid-summaries”