Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 21 min ago
PreprintCC BY 4.0HAL

A note on distribution and density estimation as a regression problem of order statistics

  • Olivier P. Faugeras
Open at sourcePDFCite

Abstract

We show how cumulative distribution function estimation (cdf) can be formulated as a regression problem, using order statistics. This results in a nonstandard nonparametric regression problem, with correlated but vanishing errors. Nonparametric regression estimators can then be leveraged to obtain corresponding estimators of the cdf and of its derivatives. We illustrate the approach, theoretically with Nadaraya-Watson regression estimator, and numerically with P-splines regression techniques. We discuss the issue of smoothing parameter selection for regression of correlated errors and show how to make use of known techniques from the regression framework to improve on the cdf and density estimation. Eventually, we draw some perspectives and show how the proposed framework could be extended to the multivariate setting.

Related

  1. Kernel Density Regression Estimation with Covariates on Riemannian Manifolds
    Gharbi Rihab, Salah Khardani, Mohamed Abdillahi Isman +1
    HALPreprintCC BY 4.0Full textStatisticsHAL
  2. Learning under Target Shift: Optimal Density Ratio Estimation and Importance-Weighted Regression
    Ren-Rui Liu, Zheng-Chu Guo
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression
    Rafael Izbicki, Pedro Luiz Coelho Rodrigues
    Transactions on Machine Learning ResearchPeer-reviewedCC BY 4.0Full textStatisticsHAL
  4. Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
    Lorenzo Tedesco, Francesco Finazzi
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. Serre's problem on statistics of Brauer symbols
    Efthymios Sofos
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{faugeras2026note,
  title = {{A note on distribution and density estimation as a regression problem of order statistics}},
  author = {Olivier P. Faugeras},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05739692v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A note on distribution and density estimation as a regression problem of order statistics
AU  - Olivier P. Faugeras
PY  - 2026
DA  - 2026/09/04
PB  - HAL
UR  - https://hal.science/hal-05739692v1
AB  - We show how cumulative distribution function estimation (cdf) can be formulated as a regression problem, using order statistics. This results in a nonstandard nonparametric regression problem, with correlated but vanishing errors. Nonparametric regression estimators can then be leveraged to obtain corresponding estimators of the cdf and of its derivatives. We illustrate the approach, theoretically with Nadaraya-Watson regression estimator, and numerically with P-splines regression techniques. We discuss the issue of smoothing parameter selection for regression of correlated errors and show how to make use of known techniques from the regression framework to improve on the cdf and density estimation. Eventually, we draw some perspectives and show how the proposed framework could be extended to the multivariate setting.
ER  -