Pith Number

pith:XIZINNM4

pith:2026:XIZINNM4K6ZGMGZLM426JUBCIF

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Estimation and Inference for the $\tau$-Quantile of Individual Heterogeneous Coefficient

Antonio F. Galvao, Jiahao Lin, Ulrich Hounyo

A two-step procedure estimates the τ-quantile of individual slope coefficients in panel data at rate √N.

arxiv:2605.01923 v2 · 2026-05-03 · econ.EM · math.ST · stat.TH

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:02:34.516424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba3286b59c57b2661b2b6735e4d022417f0c995a4e27fce775ebe39a727fe3ac

Aliases

arxiv: 2605.01923 · arxiv_version: 2605.01923v2 · doi: 10.48550/arxiv.2605.01923 · pith_short_12: XIZINNM4K6ZG · pith_short_16: XIZINNM4K6ZGMGZL · pith_short_8: XIZINNM4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XIZINNM4K6ZGMGZLM426JUBCIF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ba3286b59c57b2661b2b6735e4d022417f0c995a4e27fce775ebe39a727fe3ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "187bfae644a925e825755fcd74cb656725b077315f0c3953270a2d4dc46adc85",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "econ.EM",
    "submitted_at": "2026-05-03T15:07:21Z",
    "title_canon_sha256": "29d3f1b02936e23d0d90565f55f5aed07961e70617c67a36cbdf49139e3ca3b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01923",
    "kind": "arxiv",
    "version": 2
  }
}