{"paper":{"title":"Estimation and Inference for the $\\tau$-Quantile of Individual Heterogeneous Coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A two-step procedure estimates the τ-quantile of individual slope coefficients in panel data at rate √N.","cross_cats":["math.ST","stat.TH"],"primary_cat":"econ.EM","authors_text":"Antonio F. Galvao, Jiahao Lin, Ulrich Hounyo","submitted_at":"2026-05-03T15:07:21Z","abstract_excerpt":"This paper proposes estimation and inference procedures for the quantiles of individual heterogeneous slope coefficients within panel data. We develop a two-step quantile estimation framework for analyzing heterogeneity in individual coefficients. Unlike conventional panel quantile regression, which focuses on outcome heterogeneity, our approach targets the $\\tau$-quantile of the cross-sectional distribution of individual-specific slopes. We establish asymptotic theory under both stochastic and deterministic designs, with convergence rates $\\sqrt{N}$ and $\\sqrt{N\\sqrt{T}}$, respectively. We al"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop a two-step quantile estimation framework for analyzing heterogeneity in individual coefficients... establish asymptotic theory under both stochastic and deterministic designs, with convergence rates √N and √N√T, respectively. We also develop two corresponding bootstrap procedures for practical inference, and formally establish their validity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The methods require weaker sample size growth conditions than standard fixed-effect quantile regression and accommodate large N settings; the precise regularity conditions on the panel structure, dependence, and design that underpin the √N and √N√T rates are not detailed in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A two-step quantile estimator is proposed for the τ-quantile of heterogeneous individual slopes in panel data, with √N and √N√T rates and valid bootstrap inference.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A two-step procedure estimates the τ-quantile of individual slope coefficients in panel data at rate √N.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a9780d365f645a15a9369d5e322f97c536d7e52ee05814971fb34b93878704fc"},"source":{"id":"2605.01923","kind":"arxiv","version":2},"verdict":{"id":"549af6c6-39e0-4402-9ad7-9a39f961ceb0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T19:10:39.888350Z","strongest_claim":"We develop a two-step quantile estimation framework for analyzing heterogeneity in individual coefficients... establish asymptotic theory under both stochastic and deterministic designs, with convergence rates √N and √N√T, respectively. We also develop two corresponding bootstrap procedures for practical inference, and formally establish their validity.","one_line_summary":"A two-step quantile estimator is proposed for the τ-quantile of heterogeneous individual slopes in panel data, with √N and √N√T rates and valid bootstrap inference.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The methods require weaker sample size growth conditions than standard fixed-effect quantile regression and accommodate large N settings; the precise regularity conditions on the panel structure, dependence, and design that underpin the √N and √N√T rates are not detailed in the abstract.","pith_extraction_headline":"A two-step procedure estimates the τ-quantile of individual slope coefficients in panel data at rate √N."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01923/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T16:41:00.384169Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T04:31:22.833096Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:52:48.764300Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"084443799df888ff1284db500ece027a856daad31541b6974d23e12708d865dc"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6342cbc68e8e962e8894be20f2a52c275cc11fbc57e28dfc174416a679267bd2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}