# Variance function estimation in regression model via aggregation procedures

arXiv: https://arxiv.org/abs/2110.02715 · HTML: https://mlsanity.com/paper/2110.02715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 63 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Regression with reject option and application to kNN](https://mlsanity.com/paper/2006.16597/) (2020)
- [Adaptive estimation of High-Dimensional Signal-to-Noise Ratios](https://mlsanity.com/paper/1602.08006/) (2016)
- [Learning Heteroscedastic Models by Convex Programming under Group Sparsity](https://mlsanity.com/paper/1304.4549/) (2013)

## Abstract (arXiv)

In the regression problem, we consider the problem of estimating the variance function by the means of aggregation methods. We focus on two particular aggregation setting: Model Selection aggregation (MS) and Convex aggregation (C) where the goal is to select the best candidate and to build the best convex combination of candidates respectively among a collection of candidates. In both cases, the construction of the estimator relies on a two-step procedure and requires two independent samples. The first step exploits the first sample to build the candidate estimators for the variance function by the residual-based method and then the second dataset is used to perform the aggregation step. We show the consistency of the proposed method with respect to the L 2error both for MS and C aggregations. We evaluate the performance of these two methods in the heteroscedastic model and illustrate their interest in the regression problem with reject option.