These function calculates the generalized cross-validation criterion for the 
smoothing parameters \(\alpha_v\) or \(\alpha_w\) that are used in the 
<code>FCP_TPA</code> algorithm. As the criterion is symmetric in \(v\) and
\(w\), this function implements a generic criterion, which is called by 
<code>findAlphaVopt</code>, <code>findAlphaWopt</code> with the correct values.

internal

Calculate a multivariate functional principal component analysis
for data observed on different dimensional domains. The estimation algorithm
relies on univariate basis expansions for each element of the multivariate
functional data (Happ & Greven, 2018) <doi:10.1080/01621459.2016.1273115>.
Multivariate and univariate functional data objects are
represented by S4 classes for this type of data implemented in the package
'funData'. For more details on the general concepts of both packages and a case
study, see Happ-Kurz (2020) <doi:10.18637/jss.v093.i05>.

Clara Happ-Kurz

MFPCA

Multivariate Functional Principal Component Analysis for Data
Observed on Different Dimensional Domains

gcv function

<dl><dt>alpha</dt>
<dd>The current value of the smoothing parameter.</dd>
<dt>n</dt>
<dd>The length of the dimension, for which the smoothing parameter is to
be optimized.</dd>
<dt>z</dt>
<dd>A vector of length <code>n</code>. See Details.</dd>
<dt>eta</dt>
<dd>A vector of length <code>n</code>. See Details.</dd>
<dt>lambda</dt>
<dd>A vector of length <code>n</code>, containing the eigenvalues of the
penalty matrix corresponding the the current image direction.</dd></dl>

Arguments

Generalized cross-validation for the FCP-TPA algorithm — gcv

<dl>

<dt>alpha</dt>
<dd>The current value of the smoothing parameter.</dd>


<dt>n</dt>
<dd>The length of the dimension, for which the smoothing parameter is to
be optimized.</dd>


<dt>z</dt>
<dd>A vector of length <code>n</code>. See Details.</dd>


<dt>eta</dt>
<dd>A vector of length <code>n</code>. See Details.</dd>


<dt>lambda</dt>
<dd>A vector of length <code>n</code>, containing the eigenvalues of the
penalty matrix corresponding the the current image direction.</dd>

</dl>

gcv: Generalized cross-validation for the FCP-TPA algorithm

Description

Usage

Value

Arguments

Details

References

See Also