FLMCI

Bootstrap pointwise confidence intervals for the coefficient functions in functional linear models.

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

FLMCI function

<dl><dt>Y</dt>
<dd>Either an n-dimensional vector whose elements consist of scalar responses, or a list which contains functional responses in the form of a list LY and the time points LT at which they are observed (i.e., <code>list(Ly = LY,Lt = LT)</code>).</dd>
<dt>X</dt>
<dd>A list of lists which contains the observed functional predictors list Lxj and the time points list Ltj at which they are observed. It needs to be of the form <code>list(list(Ly = Lx1,Lt = Lxt1),list(Ly = Lx2,Lt = Lxt2),...)</code>.</dd>
<dt>level</dt>
<dd>A number taking values in [0,1] determining the confidence level. Default: 0.95.</dd>
<dt>R</dt>
<dd>An integer holding the number of bootstrap replicates. Default: 999.</dd>
<dt>optnsListY</dt>
<dd>A list of options control parameters for the response specified by <code>list(name=value)</code>. See 'Details' in FPCA.</dd>
<dt>optnsListX</dt>
<dd>A list of options control parameters for the predictors specified by <code>list(name=value)</code>. See 'Details' in FPCA.</dd></dl>

Arguments

Confidence Intervals for Functional Linear Models. — FLMCI

<dl>

<dt>Y</dt>
<dd>Either an n-dimensional vector whose elements consist of scalar responses, or a list which contains functional responses in the form of a list LY and the time points LT at which they are observed (i.e., <code>list(Ly = LY,Lt = LT)</code>).</dd>


<dt>X</dt>
<dd>A list of lists which contains the observed functional predictors list Lxj and the time points list Ltj at which they are observed. It needs to be of the form <code>list(list(Ly = Lx1,Lt = Lxt1),list(Ly = Lx2,Lt = Lxt2),...)</code>.</dd>


<dt>level</dt>
<dd>A number taking values in [0,1] determining the confidence level. Default: 0.95.</dd>


<dt>R</dt>
<dd>An integer holding the number of bootstrap replicates. Default: 999.</dd>


<dt>optnsListY</dt>
<dd>A list of options control parameters for the response specified by <code>list(name=value)</code>. See 'Details' in FPCA.</dd>


<dt>optnsListX</dt>
<dd>A list of options control parameters for the predictors specified by <code>list(name=value)</code>. See 'Details' in FPCA.</dd>

</dl>

Confidence Intervals for Functional Linear Models.

FLMCI: Confidence Intervals for Functional Linear Models.

Description

Usage

Value

Arguments

Details