A Functional Single Index Model

Jiang, Fei; Baek, Seungchul; Cao, Jiguo

doi:10.5705/ss.202018.0013

Cited by 11 publications

(9 citation statements)

References 22 publications

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“…Cai et al (2021) introduced a variable selection procedure for function‐on‐function linear models with multiple functional predictors. For more studies on function‐on‐function models and an extensive list of references, readers can refer to Goldsmith et al (2011), Scheipl et al (2015), Luo et al (2016), Lin et al (2017), Liu et al (2017), Qi and Luo (2018), Kim et al (2018), Sang et al (2018), Luo and Qi (2019), Jiang et al (2020) and Guan et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Robust penalized M‐estimation for function‐on‐function linear regression

Cai

Xue

Cao

2021

Stat

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Function-on-function linear regression is an essential tool in characterizing the linear relationship between a functional response and a functional predictor. However, most of the estimation methods for this model are based on the least-squares procedure, which is sensitive to atypical observations. In this paper, we present a robust method for the function-on-function linear model using M-estimation and penalized spline regression. A fast iterative algorithm is provided to compute the estimates. The efficiency of the proposed robust penalized M-estimator is investigated with several simulation studies in comparison with the conventional method. We demonstrate the performance of the proposed robust method with two real data examples in a capital bike-sharing study and a Hawaii ocean time-series program.functional data, penalized regression, robust procedures | INTRODUCTIONAdvancements in data collection and storage technology have enabled experimenters to collect complex and high-dimensional datasets, such as curves, images or other objects over multiple time or spatial points. This type of data is called functional data and has been encountered frequently in many scientific fields such as ecology, geophysics and medical sciences; see Ramsay and Silverman (2005), Ferraty and Vieu (2006), Horváth and Kokoszka (2012) and Zhu et al. (2012 for a general overview of functional data analysis (FDA).

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Section: Introductionmentioning

confidence: 99%

Robust penalized M‐estimation for function‐on‐function linear regression

Cai

Xue

Cao

2021

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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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“…This kind of variable is therefore called a functional variable, and the data for the variable are called functional data (Ramsay and Silverman, 2002;Morris, 2015). One of the most important functional regressions is the functional linear model, which describes the relationship of some functional covariates and scalar responses (Cardot et al, 1999(Cardot et al, , 2003Hall and Horowitz, 2007;Hilgert et al, 2013;Jiang and Wang, 2011;Jiang et al, 2020;Li and Zhu, 2020).…”

Section: Introductionmentioning

confidence: 99%

Functional L-Optimality Subsampling for Massive Data

Liu,

You,

Cao

2021

Preprint

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Massive data bring the big challenges of memory and computation to researchers, which can be tackled to some extent by taking subsamples from the full data as a surrogate. For functional data, it is common to collect measurements intensively over their domains, which require more memory and computation time when the sample size is large. The situation would be much worse when the statistical inference is made through bootstrap samples. To the best of our knowledge, there is no work to study the subsampling for the functional linear regression or its generation systematically. In this article, based on the functional L-optimality criterion we propose an optimal subsampling method for the functional linear model. When the response is a discrete or categorical variable, we further extend this subsampling method to the functional generalized linear model. We establish the asymptotic properties of the resultant estimators by the subsampling methods. The finite sample performance of our proposed subsampling methods is investigated by extensive simulation studies. We also apply our proposed subsampling methods to analyze the global climate data and the kidney transplant data. The results from the analysis of these data show that the optimal subsampling methods motivated by the functional L-optimality criterion are much better than the uniform subsampling method and can well approximate the results based on full data.

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A Functional Single Index Model

Cited by 11 publications

References 22 publications

Robust penalized M‐estimation for function‐on‐function linear regression

Robust penalized M‐estimation for function‐on‐function linear regression

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

Functional L-Optimality Subsampling for Massive Data

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