A Note on Distribution and Density Estimation as a Regression Problem of Order Statistics

Olivier Faugeras

No 26-1770, TSE Working Papers from Toulouse School of Economics (TSE)

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 van- ishing errors. Nonparametric regression estimators can then be leveraged to obtain corresponding estimators of the cdf and of its derivatives. We illus- trate 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.

Date: 2026-09
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... 2026/wp_tse_1770.pdf Full Text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:132133

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().