Content deleted Content added
No edit summary |
No edit summary |
||
Line 2:
<!-- EDIT BELOW THIS LINE -->
= Functional regression =
'''Functional regression''' is an extension of the [[Regression analysis|traditional multivariate regression]] with scalar [[Dependent and independent variables|responses]] and scalar [[Dependent and independent variables|covariates]], which allows one to conduct regression analysis on [[Functional data analysis|functional data]]. One the one hand, functional regression models can be classified into three types based on whether the responses or covariates are functional or scalar: (i) scalar responses with functional covariates, (ii) functional responses with scalar covariates, (iii) functional responses with functional covariates, and (iv) scalar or functional responses with functional and scalar covariates. On the other hand, functional regression models can be [[Linear regression|linear]], partially linear, or [[Nonlinear regression|nonlinear]]. In particular, functional polynomial models, functional [[Semiparametric_regression#Index_models|single and multiple single models]] and functional [[Additive model|additive models]] are three special cases of functional nonlinear models.
== Functional linear models (FLMs) ==
Functional linear models (FLMs) are an extension of [[Linear regression|traditional multivariate linear models]] with scalar response <math>Y\in\mathbb{R}</math> and scalar covariates <math>X∈ℝ^p</math>, which can be written as
| |||