# Robust functional regression based on principal components

arXiv: https://arxiv.org/abs/1807.00135 · HTML: https://mlsanity.com/paper/1807.00135/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [Errors-in-variables Fr'echet Regression with Low-rank Covariate Approximation](https://mlsanity.com/paper/2305.09282/) (2023)
- [Functional Output Regression with Infimal Convolution: Exploring the Huber and ε-insensitive Losses](https://mlsanity.com/paper/2206.08220/) (2022)

## Abstract (arXiv)

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and therefore are sensitive to atypical observations. To remedy this, we propose a two-step estimation procedure that combines robust functional principal components and robust linear regression. Moreover, we propose a transformation that reduces the curvature of the estimators and can be advantageous in many settings. For these estimators we prove Fisher-consistency at elliptical distributions and consistency under mild regularity conditions. The influence function of the estimators is investigated as well. Simulation experiments show that the proposed estimators have reasonable efficiency, protect against outlying observations, produce smooth estimates and perform well in comparison to existing approaches.