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PreprintarXiv licencearXiv

Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure

  • Masamune Iwasawa
  • Hayato Nakanishi
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Abstract

Researchers often observe group quantiles but not group means, raising the question of whether these summaries alone support conventional regression analysis. We develop estimation and inference methods for linear models of group means under quantile-only and mixed disclosure. We establish conditions on disclosure design for consistent estimation and asymptotic normality at the parametric rate. Under fixed disclosure, we characterize sharp identified sets and construct simultaneous confidence regions, clarifying how informativeness depends on the number and placement of disclosed quantiles. Applications to education, social care, and medical expenditure illustrate the methods. The R package qonlyreg implements the proposed procedures.

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Cite

BibTeXRIS
BibTeX
@misc{iwasawa2026quantileonly,
  title = {{Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure}},
  author = {Masamune Iwasawa and Hayato Nakanishi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27224},
  eprint = {2610.27224},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27224},
}
RIS
TY  - UNPB
TI  - Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure
AU  - Masamune Iwasawa
AU  - Hayato Nakanishi
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27224
UR  - https://arxiv.org/abs/2610.27224
AB  - Researchers often observe group quantiles but not group means, raising the question of whether these summaries alone support conventional regression analysis. We develop estimation and inference methods for linear models of group means under quantile-only and mixed disclosure. We establish conditions on disclosure design for consistent estimation and asymptotic normality at the parametric rate. Under fixed disclosure, we characterize sharp identified sets and construct simultaneous confidence regions, clarifying how informativeness depends on the number and placement of disclosed quantiles. Applications to education, social care, and medical expenditure illustrate the methods. The R package qonlyreg implements the proposed procedures.
ER  -