# Naive Penalized Spline Estimators of Derivatives Achieve Optimal Rates of Convergence

arXiv: https://arxiv.org/abs/2208.10664 · HTML: https://mlsanity.com/paper/2208.10664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 35 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems](https://mlsanity.com/paper/2507.20072/) (2025)

## Abstract (arXiv)

This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding derivative achieves the optimal L2 rate of convergence.