Functional linear models for functional responses

1997 ◽  
pp. 179-197
Author(s):  
J. O. Ramsay ◽  
B. W. Silverman
Keyword(s):  
Linear Models ◽  
Functional Responses ◽  
Functional Linear Models

scholarly journals Estimation of Causal Functional Linear Regression Models

2017 ◽  
Vol 9 (6) ◽  
pp. 106
Author(s):  
J.C.S. De Miranda
Keyword(s):  
Linear Regression ◽  
Tensor Product ◽  
Linear Regression Model ◽  
Regression Models ◽  
Linear Models ◽  
Linear Regression Models ◽  
Functional Responses ◽  
Functional Linear Models ◽  
Triangular Region ◽  
Functional Linear Regression

We present a methodology for estimating causal functional linear models using orthonormal tensor product expansions. More precisely, we estimate the functional parameters $\alpha$ and $\beta$ that appear in the causal functional linear regression model:$$\mathcal{Y}(s)=\alpha(s)+\int_a^b\beta(s,t)\mathcal{X}(t)\mathrm{d}t+\mathcal{E}(s),$$ where  $\mbox{supp } \beta \subset \mathfrak{T},$ and $\mathfrak{T}$ is the closed triangular region whose vertexes are $(a,a) , (b,a)$ and $(b,b).$ We assume we have an independent sample $\{ (\mathcal{Y}_k,\mathcal{X}_k) : 1\le k \le N, k\in \mathbb{N}\}$ of observations where the $\mathcal{X}_k $'s are functional covariates, the $\mathcal{Y}_k$'s are time order preserving functional responses and $\mathcal{E}_k,$ $1\le k \le N,$ is i.i.d. zero mean functional noise.

scholarly journals Quantifying flow–ecology relationships with functional linear models

2014 ◽  
Vol 59 (3-4) ◽  
pp. 629-644 ◽  
Author(s):  
Ben Stewart-Koster ◽  
Julian D. Olden ◽  
Keith B. Gido
Keyword(s):  
Linear Models ◽  
Functional Linear Models

scholarly journals Functional linear models for interval-valued data

2020 ◽  
pp. 1-20
Author(s):  
Ufuk Beyaztas ◽  
Han Lin Shang ◽  
Abdel-Salam G. Abdel-Salam
Keyword(s):  
Linear Models ◽  
Functional Linear Models ◽  
Interval Valued

scholarly journals Nonparametric inference in generalized functional linear models

2015 ◽  
Vol 43 (4) ◽  
pp. 1742-1773 ◽  
Author(s):  
Zuofeng Shang ◽  
Guang Cheng
Keyword(s):  
Linear Models ◽  
Nonparametric Inference ◽  
Functional Linear Models
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