Robust Function-on-Function Regression

Hullait, Harjit; Leslie, David S.; Pavlidis, Nicos G.; King, Steve

doi:10.1080/00401706.2020.1802350

Cited by 15 publications

(12 citation statements)

References 27 publications

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“…Our numerical results show that the proposed method is robust to outliers and improves prediction performance compared to the available methods when outliers are present in the data. Also, our results show that the proposed robust FPLS approach produces competitive or even better results with those of the RFPC method of Hullait et al (2021).…”

Section: Introductionmentioning

confidence: 76%

“…The simple FFLRM is constructed for both scenarios, and the bivariate coefficient is estimated using the proposed method and RFPC based on K = 15 B-spline basis functions. Similar to Hullait et al (2021), the following mean squared error (MSE) is considered to compare the performance of the methods:…”

Section: Case-2mentioning

confidence: 99%

“…Various Monte Carlo experiments under different data generating processes are conducted to evaluate the finite-sample performance of the proposed method. The results are compared with those obtained via the LS, naïve SIMPLS, and the RFPC of Hullait et al (2021). Throughout the experiments, the following FFLRM is considered:…”

Section: Monte Carlo Experimentsmentioning

confidence: 99%

“…In the context of FFLRM, Gervini (2012) proposed an outlierresistant loss function-based robust method. Also, Hullait et al (2021) proposed a Fisher-consistent robust regression model, and they proposed a robust functional principal component (RFPC)-based estimator to estimate the model parameter. However, these two methods are based on the simple FFLRM, with only one predictor in the model.…”

Section: Introductionmentioning

confidence: 99%

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

Beyaztaş

Shang

2021

Comput Stat

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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 robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

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Section: Introductionmentioning

confidence: 76%

Section: Case-2mentioning

confidence: 99%

Section: Monte Carlo Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Beyaztaş

Shang

2021

Comput Stat

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“…Next, using a similar parameterization as in Chiou et al (2016); Hullait et al (2021) and by orthonormalities of φ(t) and ψ m (s), the τ th conditional quantile of the response function in (2) can be expressed as follows:…”

Section: Methodsmentioning

confidence: 99%

Function-on-function linear quantile regression

Beyaztaş¹,

Shang²

2021

Preprint

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In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models.

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Adaptive smoothing spline estimator for the function-on-function linear regression model

et al. 2022

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In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the package , openly available online on CRAN.

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Robust Function-on-Function Regression

Cited by 15 publications

References 27 publications

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

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

Function-on-function linear quantile regression

Adaptive smoothing spline estimator for the function-on-function linear regression model

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