Sharp Interval Widths for Rasch Queries with Drift Chosen before Randomization

For two Rasch item types with one fixed common calibration offset bounded by a and opposite time-varying drift bounded by r, drift commitment before a fresh private item choice gives the sharp universal asymptotic interval diameter 2a + log(cosh r). The note proves anytime coverage, a per-model almost-sure upper cap without convergence of drift averages, and matching complete-observation-law lower experiments for every adaptive strategy. It also provides complete comparisons with revealed selection and paired responses. Technical note. AI tools assisted with mathematical derivation, drafting, and internal proof review.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23683454
Primary Topic
Psychometric Methodologies and Testing
Type
preprint
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preprint

Sharp Interval Widths for Rasch Queries with Drift Chosen before Randomization

Zihuan Xu
Zenodo (CERN European Organization for Nuclear Research)
Psychometric Methodologies and Testing
preprint

Sharp Interval Widths for Rasch Queries with Drift Chosen before Randomization

Zihuan Xu
preprint en

Abstract

For two Rasch item types with one fixed common calibration offset bounded by a and opposite time-varying drift bounded by r, drift commitment before a fresh private item choice gives the sharp universal asymptotic interval diameter 2a + log(cosh r). The note proves anytime coverage, a per-model almost-sure upper cap without convergence of drift averages, and matching complete-observation-law lower experiments for every adaptive strategy. It also provides complete comparisons with revealed selection and paired responses. Technical note. AI tools assisted with mathematical derivation, drafting, and internal proof review.

Zenodo (CERN European Organization for Nuclear Research)
Capital Normal University (CN)
Psychometric Methodologies and Testing
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