# Scalar-on-function local linear regression and beyond

arXiv: https://arxiv.org/abs/1907.08074 · HTML: https://mlsanity.com/paper/1907.08074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2019.

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

- [On projection methods for functional time series forecasting](https://mlsanity.com/paper/2105.04399/) (2021)

## Abstract (arXiv)

Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression based on a projection approach a prominent method for solving this regression problem. Our asymptotic results demonstrate that the functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, the local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object on its own. The local linear estimator of the functional derivative is shown to be consistent. On simulated datasets we illustrate good finite sample properties of both proposed methods. On a real data example of a single-functional index model we indicate how the functional derivative of the regression operator provides an original and fast, widely applicable estimating method.