Function-on-function quadratic regression models

Sun, Yifan; Wang, Qihua

doi:10.1016/j.csda.2019.106814

Cited by 13 publications

(8 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the irregular WH growth and heavy metals distribution patterns were not possible to predict using the linear models, we developed a modified cubic model (Kumar et al 2019b;Sun and Wang 2020). During the two-year study period, simulation of WH growth, heavy metals contents in water, and plant biomass were done using a polynomial cubic function.…”

Section: Mathematical Model and Verificationmentioning

confidence: 99%

Modeling of water hyacinth growth and its role in heavy metals accumulation from unoperated old Ganga canal at Haridwar, India

Kumar

Eid

et al. 2021

Rend. Fis. Acc. Lincei

View full text Add to dashboard Cite

The present study aimed to investigate the annual potential of water hyacinth (WH; Eichhornia crassipes) macrophyte in an un-operated/abandoned stretch of the upper Ganga canal at Haridwar, India. The study covered a 25 km long and 100 m wide stretch of the old Ganga canal which exhibits a huge WH growth every year. For this, standard field and laboratory methods were adopted to estimate the WH biomass density (Kg/m 2 ), and heavy metals dynamics between canal water and macrophyte biomass. Results showed that the average annual density of WH biomass was 5.538 kg/m 2 with significant (P < 0.05) heavy metals (HMs) accumulation as 1.50 mg/Kg dw of Cd, 0.21 of mg/Kg dw of Cr, 2.19 mg/Kg dw of Cu, 28.54 mg/Kg dw of Fe, 20.79 mg/Kg dw of Mn, and 9.39 mg/Kg dw of Zn, respectively. Using a polynomial cubic model, the annual trends of WH growth and HMs accumulation in both water and biomass were also simulated. The developed models showed good R 2 and error validation results that support the prediction criteria. The findings of this study revealed that WH's growth in the un-operated stretch of the old Ganga canal located at Haridwar has high HMs accumulation and biomass production potentials.

show abstract

Section: Mathematical Model and Verificationmentioning

confidence: 99%

Modeling of water hyacinth growth and its role in heavy metals accumulation from unoperated old Ganga canal at Haridwar, India

Kumar

Eid

et al. 2021

Rend. Fis. Acc. Lincei

View full text Add to dashboard Cite

show abstract

“…However, recent studies have shown that functional regression models, including a quadratic term and interaction effects, perform better than standard functional regression models in the presence of interaction (Luo and Qi, 2019;Matsui, 2020;Sun and Wang, 2020;Beyaztas and Shang, 2021a). The functional predictors' quadratic or interaction effects can also be used in the proposed method to characterize the functional response's conditional distribution.…”

Section: Discussionmentioning

confidence: 99%

Function-on-function partial quantile regression

Beyaztaş¹,

Shang²,

Alın³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…One remedy to obtain a stable estimate for Γ (3) is to use dimension-reduction techniques, such as PC or PLS regression models. PC regression has been proposed by Aguilera et al (1999) and Yao et al (2005) to estimate standard function-onfunction regression models and by Sun and Wang (2020) to estimate univariate function-on-function quadratic regression models. However, this method does not take into account the relationship between response and predictor variables when deciding the PCs.…”

Section: Methodsmentioning

confidence: 99%

“…Matsui (2020) estimated model parameters by the penalized maximum likelihood (PML) method. Sun and Wang (2020) proposed a functional principal component (PC) regression to estimate the parameters in model (1.2) and provided a procedure to test the significance of the quadratic term. Luo and Qi (2019) proposed a multiple function-on-function regression model with quadratic and interaction effects as follows:…”

Section: Introductionmentioning

confidence: 99%

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

Beyaztaş¹,

Shang²

2020

Preprint

View full text Add to dashboard Cite

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. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this difficulty, in practice, the functional data that belong to the infinite-dimensional space are generally projected into a finitedimensional space of basis functions. The function-on-function regression model is converted to a multivariate regression model of the basis expansion coefficients. In the estimation phase of the proposed method, the functional variables are approximated by a finite-dimensional basis function expansion method. We show that the partial least squares regression constructed via a functional response, multiple functional predictors, and quadratic/interaction terms of the functional predictors is equivalent to the partial least squares regression constructed using basis expansions of functional variables. From the partial least squares regression of the basis expansions of functional variables, we provide an explicit formula for the partial least squares estimate of the coefficient function of the function-on-function regression model. Because the true forms of the models are generally unspecified, we propose a forward procedure for model selection. The finite sample performance of the proposed method is examined using several Monte Carlo experiments and two empirical data analyses, and the results were found to compare favorably with an existing method.

show abstract

Function-on-function quadratic regression models

Cited by 13 publications

References 18 publications

Modeling of water hyacinth growth and its role in heavy metals accumulation from unoperated old Ganga canal at Haridwar, India

Modeling of water hyacinth growth and its role in heavy metals accumulation from unoperated old Ganga canal at Haridwar, India

Function-on-function partial quantile regression

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

Contact Info

Product

Resources

About