Decision uncertainty in particulate-matter measurement comparability under sparse reference sampling

Abstract A comparability verdict between a reference and a candidate measurement method depends on the reference observations supporting the fitted relationship. We examined how far such a verdict remains determinate when the same paired record is reduced to fewer reference dates. Lineage-consistent daily PM₂.₅ records from 45 US sites (2022–2025) supplied 127 episodes and 43,576 same-site reference–equivalent-method pairs. All phases of 1-in-3, 1-in-6 and 1-in-12 calendars were compared with each episode’s near-daily record. An ordinary least squares (OLS) slope–intercept bias envelope from the US equivalence criteria supplied point verdicts, and a circular moving-block bootstrap classified their stability. Under the primary 0.95/0.05 stability rule, 82 near-daily benchmarks (64.6%) were boundary-uncertain. On the 45 benchmark-stable episodes, site-equal sparse indeterminacy was 33.02% (95% confidence interval 21.07–46.07%), 63.77% (52.98–73.75%) and 73.81% (63.69–82.56%), and 88 of 90 point mismatches became indeterminate rather than opposite stable verdicts. Levels depended on the stability cutoff, but the ordering held at every cutoff from 0.80 to 0.99 and under data-driven and calendar-duration-matched block bootstraps, event exclusion and removal of high-concentration days. A baseline using only the near-daily record and its serial dependence reproduced the 1-in-6 and 1-in-12 levels within 4 percentage points. No additional calendar point-mismatch risk was detected relative to size-matched random sampling; an exploratory state comparison suggested lower indeterminacy than random sampling at 1-in-3. In a known-truth simulation at 1-in-12, interval coverage was about 88%; records with true parameters inside the envelope were mostly indeterminate, and 14 of their 64 stable verdicts had the wrong direction. Reporting the bootstrap state and reference support alongside the point verdict shows how much evidence a comparability verdict carries, and benchmark-based baselines may help assess how much determinacy a sparser schedule would retain.