Variable Selection for Multiple Function-on-Function Linear Regression

Cai, Xiong; Xue, Liugen; Cao, Jiguo

doi:10.5705/ss.202020.0473

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…where 𝛿𝛿 0 , 𝛿𝛿 1 𝑦𝑦 𝑘𝑘 , 𝛿𝛿 2 𝑦𝑦 𝑘𝑘 , 𝛿𝛿 3 𝑦𝑦 𝑘𝑘 are coefficients obtained by fitting linear model to the data and 𝜖𝜖 1 𝑦𝑦 𝑘𝑘 are independent functional errors. The multiple function-on-function linear model was described in detail by Acal, Escabias, Aguilera and Valderrama (2021) and by Cai, Xue and Cao (2022).…”

Section: Prediction Of the Number Of Hospitalised And Intensive Care ...mentioning

confidence: 99%

The Second Wave of the COVID-19 Pandemic in Poland - Characterised Using FDA Methods

Hęćka

2023

Econometrics

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The aim of this article was to analyse functional data of the number of hospitalised individuals, intensive care patients, positive COVID-19 tests, deaths and convalescents during the second wave of the COVID-19 pandemic in Poland. For this purpose, firstly the author convert data of sixteen voivodeships to smooth functions, and then used the principal component analysis and multiple function-on-function linear regression model to predict the number of hospitalised and intensive care patients due to the COVID-19 infection during the second wave of the pandemic. Finally, the results were compared with those previously obtained for the combined data of the second and third wave of the COVID-19 pandemic in Poland.

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Section: Prediction Of the Number Of Hospitalised And Intensive Care ...mentioning

confidence: 99%

The Second Wave of the COVID-19 Pandemic in Poland - Characterised Using FDA Methods

Hęćka

2023

Econometrics

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“…Alternatively, one can compute the functional principal component scores for

x_{i} false(t false)

and

y_{i} false(t false)

and base the estimation on the functional principal component scores (Yao, Müller & Wang, 2005; Chen & Wang, 2011; Ivanescu et al, 2015). Cai, Xue & Cao (2020) proposed a variable selection procedure for the function‐on‐function regression model using the group smoothly clipped absolute deviation regulation method. Cai, Xue & Cao (2021) presented a robust method for the function‐on‐function regression model using M‐estimation and penalized spline regression.…”

Section: Introductionmentioning

confidence: 99%

Sparse estimation of historical functional linear models with a nested group bridge approach

2022

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The conventional historical functional linear model relates the current value of the functional response at time t to all past values of the functional covariate up to time t. Motivated by situations where it is more reasonable to assume that only recent, instead of all, past values of the functional covariate have an impact on the functional response, in this work we investigate the historical functional linear model with an unknown forward time lag into the history. In addition to estimating the bivariate regression coefficient function, we also aim to identify the historical time lag from the data, which is important in many applications. To this end, we propose an estimation procedure that uses the finite element method to conform naturally to the trapezoidal domain of the bivariate coefficient function. We use a nested group bridge penalty to facilitate simultaneous estimation of the bivariate coefficient function and the historical lag, and show that our proposed estimators are consistent. We demonstrate this method of estimation in a real data example investigating the effect of muscle activation recorded via the noninvasive electromyography (EMG) method on lip acceleration during speech production. In addition, we examine the finite sample performance of our proposed method in comparison with the conventional approach to estimation via simulation studies.

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“…This practical problem inspires us to capture the dynamic behaviour of a set of scalar predictors of interest on the functional response. Function-on-scalar regression, which characterizes the relationship between a functional response and a set of scalar predictors, is an integral part of functional data analysis (Ramsay & Silverman, 2005;Ferraty & Vieu, 2006;Cao & Ramsay, 2010;Ainsworth, Routledge & Cao, 2011;Liu, Wang & Cao, 2017;Lin et al, 2017;Guan, Lin & Cao, 2020;Jiang et al, 2020;Cai, Xue & Cao, 2021). Function-on-scalar regression has become increasingly popular in the analysis of gene expression data and imaging data (see, e.g., Wang, Chen & Li, 2007;Li, Huang & Zhu, 2017).…”

Section: Introductionmentioning

confidence: 99%

Robust estimation and variable selection for function‐on‐scalar regression

2021

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Function-on-scalar regression is commonly used to model the dynamic behaviour of a set of scalar predictors of interest on the functional response. In this article, we develop a robust variable selection procedure for function-on-scalar regression with a large number of scalar predictors based on exponential squared loss combined with the group smoothly clipped absolute deviation regularization method. The proposed procedure simultaneously selects relevant predictors and provides estimates for the functional coefficients, and achieves robustness and efficiency using tuning parameters selected by a data-driven procedure. Under reasonable conditions, we establish the asymptotic properties of the proposed estimators, including estimation consistency and the oracle property. The finite-sample performance of the proposed method is investigated with simulation studies. The proposed method is also demonstrated with a real diffusion tensor imaging data example.

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Variable Selection for Multiple Function-on-Function Linear Regression

Cited by 7 publications

References 37 publications

The Second Wave of the COVID-19 Pandemic in Poland - Characterised Using FDA Methods

The Second Wave of the COVID-19 Pandemic in Poland - Characterised Using FDA Methods

Sparse estimation of historical functional linear models with a nested group bridge approach

Robust estimation and variable selection for function‐on‐scalar regression

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