Functional Linear Models. Extend linear model ideas to FDA linear regression ANOVA. Outline. Chapter 9 Introduce functional linear model Fitting the model Assessing the fit Computational issues. Functional linear models. In formal term: Inner product representation: Matrix version:.
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Extend linear model ideas to FDA
Reinterpret the squared norm
The goal is to estimate LMSSE()
Minimizing the regularized RSS
Modeling with basis expansions1. Choosing a K-vector of linearly independent functions2. Representing observed Y and estimatedparameter 3. The matrix system of linear equations
Perfectly fit without error at all
Use regularization to identify uniquely
a. re-expressing the model and data
b. smoothing by basis truncation
Higher precipitation is associated with higher temperatures in the last three months of the year and with lower temperatures in spring and early summer.