Functional regression: Difference between revisions

Revision as of 07:10, 11 March 2017

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== Extensions ==

A direct extension of functional linear models with scalar response is to add a link function to create a [[Generalized functional linear model|generalized functional linear model]] (GFLM) by analogy to extending [[Linear regression|linear regression]] to [[Generalized linear model|generalized linear regression]] (GLM), of which the three components are:

# Linear predictor <math>\eta display="block">Y=g\left( \beta_0 + \int_{\mathcal{T}} X^c(t)\beta(t)dt\right) +\epsilon</math>;

# Variance function <math>\text{Var}(Y|X) = V(\mu)</math>, where <math>\mu = \mathbb{E}(Y|X)</math> is the [[Conditional expectation|conditional mean]];

where <math>g</math> is a pre-specific link function.

# Link function <math>g</math> connecting the first two components <math>\mu=g(\eta)</math>.

== See also ==