# Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows

arXiv: https://arxiv.org/abs/2203.02997 · HTML: https://mlsanity.com/paper/2203.02997/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 60 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space](https://mlsanity.com/paper/1808.02111/) (2018)
- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)
- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [Optimal and Efficient Algorithms for General Mixable Losses against Switching Oracles](https://mlsanity.com/paper/2108.06411/) (2021)
- [Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics](https://mlsanity.com/paper/2202.11141/) (2022)

## Built on by (most cited first, 3 of 3)

- [Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity](https://mlsanity.com/paper/2203.14324/) (2022)
- [Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interference](https://mlsanity.com/paper/2204.08411/) (2022)
- [An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windows](https://mlsanity.com/paper/2206.14749/) (2022)

## Abstract (arXiv)

We investigate the optimal selection of weight windows for the problem of weighted least squares. We show that weight windows should be symmetric around its center, which is also its peak. We consider the class of tapered rectangle window weights, which are nonincreasing away from the center. We show that the best rectangle window is optimal for such window definitions. We also extend our results to the least absolutes and more general case of arbitrary loss functions to find similar results.