# Adaptive functional linear regression

@article{Comte2011AdaptiveFL, title={Adaptive functional linear regression}, author={Fabienne Comte and Jan Johannes}, journal={Annals of Statistics}, year={2011}, volume={40}, pages={2765-2797} }

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395–408] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows us to cover the prediction problem with respect to the mean squared prediction error as well as the estimation of the slope function and its…

## 53 Citations

### Adaptive estimation of linear functionals in functional linear models

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- 2011

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of randomfunctions. In Johannes…

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### Adaptive nonparametric estimation in the presence of dependence

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### PCA-based estimation for functional linear regression with functional responses

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### Lasso in infinite dimension: application to variable selection in functional multivariate linear regression

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- 2019

The model studied in this paper assumes a linear dependence between a quantity of interest and several covariates, at least one of which has an inﬁnite dimension, and proposes a coordinate descent algorithm.

### Minimax adaptive tests for the Functional Linear model

- Mathematics
- 2012

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections…

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