Local polynomial estimation of quantile density functions

Niclas Jacobsen; Natalie Neumeyer

Local polynomial estimation of quantile density functions

Statistics Theory 2026-07-17 v1 Methodology

Authors: Niclas Jacobsen , Natalie Neumeyer

Abstract

A new approach for nonparametric estimation of the quantile density function (sparsity function) and its derivatives is suggested which is based on local polynomial estimation. The estimator has more advantageous properties at the boundaries than classical quantile density estimators. Asymptotic normality is shown and the bias, asymptotic variance as well as boundary properties are compared with other estimators.

Cite

@article{arxiv.2607.16016,
  title  = {Local polynomial estimation of quantile density functions},
  author = {Niclas Jacobsen and Natalie Neumeyer},
  journal= {arXiv preprint arXiv:2607.16016},
  year   = {2026}
}