fts.dpca.var {freqdom.fda} | R Documentation |
Proportion of variance explained by dynamic principal components
Description
Computes the proportion and cumulative proportion of variance explained by dynamic principal components.
Usage
fts.dpca.var(F)
Arguments
F |
spectral density operator, provided as an object of class |
Details
Consider a spectral density operator \mathcal{F}_\omega
and let \lambda_\ell(\omega)
by the \ell
-th dynamic
eigenvalue. The proportion of variance described by the \ell
-th dynamic principal component is given as
v_\ell:=\int_{-\pi}^\pi \lambda_\ell(\omega)d\omega/\int_{-\pi}^\pi \mathrm{tr}(\mathcal{F}_\omega)d\omega
.
This function numerically computes the vectors (v_\ell)
.
For more details we refer to Hormann et al. (2015).
Value
A vector containing the v_\ell
.
References
Hormann, S., Kidzinski, L., and Hallin, M. Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77.2 (2015): 319-348.
See Also
The multivariate equivalent in the freqdom
package: dpca.var