R/pkgname.R

In hadjipantelis/tPACE: Functional Data Analysis and Empirical Dynamics

#' fdapace: Principal Analysis by Conditional Expectation and Applications in
#' Functional Data Analysis (revised version 16 August 2019)
#'
#' fdapace for Functional Data Analysis 
#' 
#' fdapace is 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 fda-pace and vice versa.
#' 
#' References: Wang, J.L., Chiou, J.,  Müller, H.G. (2016). Functional data analysis. Annual Review of Statistics and Its Application 3, 257--295
#' Chen, K., Zhang, X., Petersen, A., Müller, H.G.  (2017). Quantifying infinite-dimensional data: Functional Data Analysis in action. 
#' Statistics in Biosciences 9, 582–-604.
#' 
#' Links for fda-pace/PACE:
#' Matlab version of pace at http://anson.ucdavis.edu/~mueller/data/pace.html
#' Papers and background at http://anson.ucdavis.edu/~mueller/  and  http://www.stat.ucdavis.edu/~wang/
#' 
#' 
#' 
#' PACE is based on the idea that observed functional data
#' are generated by a sample of underlying (but usually not fully
#' observed) random trajectories that are realizations of a stochastic process. It does not rely on pre-smoothing of
#' trajectories, which is problematic if functional data are sparsely sampled.
#' 
#' The functional principal components can be used for further statistical analysis depending on 
#' the demands of a user, for example if one has densely sampled functional predictors and a generalized 
#' response, such as in a GLM, the predictor functions can be replaced by their first couple of principal component scores that
#' will then be used as predictors; one can also easily fit polynomial functional models by using powers (usually squares) 
#' and interactions of functional principal 
#' components among the predictors for a scalar response. 
#' 
#' fda-pace is a comprehensive package that directly implements fitting of the following models:
#' -- functional linear regression 
#' -- functional additive regression
#' -- functional covariance and correlation (via dynamic correlation) 
#' -- functional clustering 
#' -- concurrent (varying coefficient) regression models for sparse and dense designs
#' -- varying coefficient additive models
#' -- multivariate functional data analysis (normalization and functional singular component analysis)
#' -- variance processes and volatility processes (the latter of interest in finance)
#' -- optimal designs for longitudinal data analysis (for trajectory prediction and for functional linear regression) 
#' -- stringing, a method to convert high-dimensional data into functional data
#' -- quantile regression, with functions as predictors
#'  
#'  
#' 
#' Maintainer:  Yaqing Chen \email{yaqchen@@ucdavis.edu}
#' 
#' @author
#' Yaqing Chen \email{yaqchen@@ucdavis.edu}
#' Cody Carroll \email{cjcarroll@@ucdavis.edu}
#' Xiongtao Dai \email{dai@@ucdavis.edu}
#' Jianing Fan
#' Pantelis Z. Hadjipantelis 
#' Kyunghee Han 
#' Hao Ji
#'  
#' Hans-Georg Müller \email{hgmueller@@ucdavis.edu}
#' Jane-Ling Wang \email{janelwang@@ucdavis.edu}
#'
#'
#' 
#'
#' @docType package
#' @name fdapace
#' @useDynLib fdapace
#' @import Rcpp
#' @importFrom Matrix Matrix
#' @importFrom Hmisc approxExtrap
#' @importFrom pracma meshgrid midpoint mod ones uniq
#' @importFrom numDeriv grad hessian
#' @importFrom grDevices colorRampPalette dev.new palette
#' @importFrom graphics abline barplot boxplot grid legend lines matlines matplot par plot points polygon 
#' @importFrom stats aggregate approx approxfun binomial cov dist fitted glm kmeans lm median na.omit optim predict quantile rnorm runif spline var sd poly weighted.mean cor dunif
#' @importFrom utils head tail
#' @importFrom MASS isoMDS mvrnorm
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