# Functional Data Analysis

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## Definition

Functional data is multivariate data with an ordering on the dimensions.

Key assumption: **smoothness**

with $t$ in a continuum (usually time), and $x_i(t)$ smooth.

Functional data = the functions $x_i(t)$.

## Interests

- Representations of distribution of functions
- mean
- variation
- covariation

- Relationships of functional data to
- covariates
- responses
- other functions

- Relationships between derivatives of functions
- Timing of events in functions