Determine an appropriate LSCP bandwidth in practice

Determine the bandwidth for the localized global spatial conformal prediction (LSCP) procedure that appropriately balances empirical coverage and interval width across target locations and sampling geometries.

Background

Localized global spatial conformal prediction (LSCP) assigns greater weight to calibration observations near the target to address failures of exchangeability caused by nonrandom spatial geometry. Its bandwidth parameter controls the degree of localization: very small bandwidths can produce unbounded intervals because too few calibration observations receive substantial weight, whereas large bandwidths make LSCP approach the global spatial conformal prediction (GSCP) method and may leave coverage failures unresolved.

The paper’s two-cluster example demonstrates that the bandwidth entails a practical trade-off. Intermediate values can improve coverage but produce wider intervals, while larger values narrow the interval toward GSCP and can retain undercoverage under distant calibration. The authors explicitly state that the bandwidth achieving the desired balance is unknown in practice.