# A robust partial least squares approach for function-on-function regression

@article{Beyaztas2022ARP, title={A robust partial least squares approach for function-on-function regression}, author={Ufuk Beyaztas and Han Lin Shang}, journal={Brazilian Journal of Probability and Statistics}, year={2022} }

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A…

## References

SHOWING 1-10 OF 66 REFERENCES

### On function-on-function regression: partial least squares approach

- Mathematics, Computer ScienceEnvironmental and Ecological Statistics
- 2020

In the proposed method, the B -spline basis functions are utilized to convert discretely observed data into their functional forms and generalized cross-validation is used to control the degrees of roughness.

### A partial least squares approach for function-on-function interaction regression

- MathematicsComput. Stat.
- 2021

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects and a forward procedure for model selection is proposed.

### Robust Function-on-Function Regression

- Computer Science, MathematicsTechnometrics
- 2021

A Fisher-consistent robust functional linear regression model that is able to effectively fit data in the presence of outliers is introduced that can be used alongside an outlier detection procedure to effectively identify abnormal functional responses.

### Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

- Mathematics
- 2017

Functional data analysis is a field of growing importance in Statistics. In particular, the functional linear model with scalar response is surely the model that has attracted more attention in both…

### Functional Additive Models

- Mathematics
- 2008

In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means that the response is a linear function…

### Robust methods for partial least squares regression

- Environmental Science
- 2003

Partial least squares regression (PLSR) is a linear regression technique developed to deal with high‐dimensional regressors and one or several response variables. In this paper we introduce…

### Robust functional linear regression based on splines

- Computer ScienceComput. Stat. Data Anal.
- 2013

### An RKHS approach to robust functional linear regression

- Mathematics, Computer Science
- 2016

It is shown that the theoretical properties of robust estimators for the regression coefficient function in thefunctional linear regression achieve the same convergence rate for both prediction and estimation as the penalized least squares estimator in the classical functional linear regression.