GetCrCovYZ

Calculate the raw and the smoothed cross-covariance between functional
and scalar predictors using bandwidth bw or estimate that bw using GCV

A versatile package that provides implementation of various
methods of Functional Data Analysis (FDA) and Empirical Dynamics. The core of this
package is Functional Principal Component Analysis (FPCA), a key technique for
functional data analysis, for sparsely or densely sampled random trajectories
and time courses, via the Principal Analysis by Conditional Estimation
(PACE) algorithm. This core algorithm yields covariance and mean functions,
eigenfunctions and principal component (scores), for both functional data and
derivatives, for both dense (functional) and sparse (longitudinal) sampling designs.
For sparse designs, it provides fitted continuous trajectories with confidence bands,
even for subjects with very few longitudinal observations. PACE is a viable and
flexible alternative to random effects modeling of longitudinal data. There is also a
Matlab version (PACE) that contains some methods not available on fdapace and vice
versa. Updates to fdapace were supported by grants from NIH Echo and NSF DMS-1712864 and DMS-2014626.
Please cite our package if you use it (You may run the command citation("fdapace") to get the citation format and bibtex entry).
References: Wang, J.L., Chiou, J., Müller, H.G. (2016) <doi:10.1146/annurev-statistics-041715-033624>; Chen, K., Zhang, X., Petersen, A., Müller, H.G. (2017) <doi:10.1007/s12561-015-9137-5>.

Yidong Zhou

fdapace

Functional Data Analysis and Empirical Dynamics

Han Chen

Su I Iao

Poorbita Kundu

Hang Zhou

Satarupa Bhattacharjee

Cody Carroll

Yaqing Chen

Xiongtao Dai

Jianing Fan

Alvaro Gajardo

Pantelis Z. Hadjipantelis

Kyunghee Han

Hao Ji

Changbo Zhu

Paromita Dubey

Shu-Chin Lin

Hans-Georg Müller

Jane-Ling Wang

GetCrCovYZ function

<dl><dt>bw</dt>
<dd>Scalar bandwidth for smoothing the cross-covariance function (if NULL it will be automatically estimated)</dd>
<dt>Z</dt>
<dd>Vector N-1 Vector of length N with the scalar function values</dd>
<dt>Zmu</dt>
<dd>Scalar with the mean of Z (if NULL it will be automatically estimated)</dd>
<dt>Ly</dt>
<dd>List of N vectors with amplitude information</dd>
<dt>Lt</dt>
<dd>List of N vectors with timing information</dd>
<dt>Ymu</dt>
<dd>Vector Q-1 Vector of length nObsGrid containing the mean function estimate</dd>
<dt>support</dt>
<dd>Vector of unique and sorted values for the support of the smoothed cross-covariance function (if NULL it will be automatically estimated)</dd>
<dt>kern</dt>
<dd>Kernel type to be used. See ?FPCA for more details. (default: 'gauss')
If the variables Ly1 is in matrix form the data are assumed dense and only
the raw cross-covariance is returned. One can obtain Ymu1 
from <code>FPCA</code> and <code>ConvertSupport</code>.</dd></dl>

Arguments

Functional Cross Covariance between longitudinal variable Y and scalar variable Z — GetCrCovYZ

<dl>

<dt>bw</dt>
<dd>Scalar bandwidth for smoothing the cross-covariance function (if NULL it will be automatically estimated)</dd>


<dt>Z</dt>
<dd>Vector N-1 Vector of length N with the scalar function values</dd>


<dt>Zmu</dt>
<dd>Scalar with the mean of Z (if NULL it will be automatically estimated)</dd>


<dt>Ly</dt>
<dd>List of N vectors with amplitude information</dd>


<dt>Lt</dt>
<dd>List of N vectors with timing information</dd>


<dt>Ymu</dt>
<dd>Vector Q-1 Vector of length nObsGrid containing the mean function estimate</dd>


<dt>support</dt>
<dd>Vector of unique and sorted values for the support of the smoothed cross-covariance function (if NULL it will be automatically estimated)</dd>


<dt>kern</dt>
<dd>Kernel type to be used. See ?FPCA for more details. (default: 'gauss')
If the variables Ly1 is in matrix form the data are assumed dense and only
the raw cross-covariance is returned. One can obtain Ymu1 
from <code>FPCA</code> and <code>ConvertSupport</code>.</dd>

</dl>

Functional Cross Covariance between longitudinal variable Y and scalar variable Z

GetCrCovYZ: Functional Cross Covariance between longitudinal variable Y and scalar variable Z

Description

Usage

Value

Arguments

References

Examples