R/fda.usc-package.R

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

#' Functional Data Analysis and Utilities for Statistical Computing (fda.usc)
#' 
#' This devel version carries out exploratory and descriptive analysis of functional
#' data exploring its most important features: such as depth measurements or
#' functional outliers detection, among others. \cr It also helps to explain
#' and model the relationship between a dependent variable and independent
#' (regression models) and make predictions. Methods for supervised or
#' unsupervised classification of a set of functional data regarding a feature
#' of the data are also included. Finally, it can perform analysis of variance
#' model (ANOVA) for functional data.
#' 
#' Sections of fda.usc-package: \cr 
#' \tabular{ll}{ 
#' \tab A.- Functional Data Representation \cr
#' \tab B.- Functional Outlier Detection \cr
#' \tab C.- Functional Regression Model \cr
#' \tab D.- Functional Supervised  Classification  \cr
#' \tab E.- Functional Non-Supervised Classification \cr
#' \tab F.- Functional ANOVA \cr
#' \tab G.- Auxiliary functions\cr
#'  }
#' 
#' A.- Functional Data Representation \cr The functions included in this
#' section allow to define, transform, manipulate and represent a functional
#' dataset in many ways including derivatives, non-parametric kernel methods or
#' basis representation.\cr
#' 
#' \tabular{ll}{ \tab \code{\link{fdata}} \cr \tab \code{\link{plot.fdata}} \cr
#' \tab \code{\link{fdata.deriv}} \cr \tab \code{\link{CV.S}} \cr \tab
#' \code{\link{GCV.S}} \cr \tab \code{\link{optim.np}} \cr \tab
#' \code{\link{optim.basis}} \cr \tab \code{\link{S.NW}} \cr \tab
#' \code{\link{S.LLR}} \cr \tab \code{\link{S.basis}} \cr \tab
#' \code{\link{Var.e}} \cr \tab \code{\link{Var.y}} \cr }
#' 
#' B.- Functional Depth and Functional Outlier Detection \cr
#' 
#' The functional data depth calculated by the different depth functions
#' implemented that could be use as a measure of centrality or outlyingness.\cr
#' \cr B.1-Depth methods \code{\link{Depth}}:\cr \tabular{ll}{ \tab
#' \code{\link{depth.FM}} \cr \tab \code{\link{depth.mode}} \cr \tab
#' \code{\link{depth.RP}} \cr \tab \code{\link{depth.RT}} \cr \tab
#' \code{\link{depth.RPD}} \cr \tab \code{\link{Descriptive}} \cr }
#' B.2-Functional Outliers detection methods:\cr \tabular{ll}{ \tab
#' \code{\link{outliers.depth.trim}} \cr \tab \code{\link{outliers.depth.pond}}
#' \cr \tab \code{\link{outliers.thres.lrt}} \cr \tab
#' \code{\link{outliers.lrt}} \cr } C.- Functional Regression Models\cr
#' 
#' C.1. Functional explanatory covariate and scalar response\cr The functions
#' included in this section allow the estimation of different functional
#' regression models with a scalar response and a single functional explicative
#' covariate.\cr \tabular{ll}{ \tab \code{\link{fregre.pc}} \cr \tab
#' \code{\link{fregre.pc.cv}} \cr \tab \code{\link{fregre.pls}} \cr \tab
#' \code{\link{fregre.pls.cv}} \cr \tab \code{\link{fregre.basis}} \cr \tab
#' \code{\link{fregre.basis.cv}} \cr \tab \code{\link{fregre.np}} \cr \tab
#' \code{\link{fregre.np.cv}} \cr }
#' 
#' C.2. Test for the functional linear model (FLM) with scalar response.\cr
#' \tabular{ll}{ \tab \code{\link{flm.Ftest}}, F-test for the FLM with scalar
#' response \cr \tab \code{\link{flm.test}}, Goodness-of-fit test for the FLM
#' with scalar response \cr \tab \code{\link{PCvM.statistic}}, PCvM statistic
#' for the FLM with scalar response \cr }
#' 
#' C.3. Functional and non functional explanatory covariates.\cr The functions
#' in this section extends those regression models in previous section in
#' several ways.
#' 
#' \tabular{ll}{ 
#' \tab \code{\link{fregre.plm}}: Semifunctional Partial Linear Regression (an extension of  \code{\link{lm}} model)\cr 
#' \tab \code{\link{fregre.lm}}: Functional Linear Regression (an extension of  \code{\link{lm}} model) \cr 
#' \tab \code{\link{fregre.glm}}: Functional Generalized Linear Regression (an extension of  \code{\link{glm}} model) \cr 
#' \tab \code{\link{fregre.gsam}}: Functional Generalized Spectral Additive Regression  (an extension of  \code{\link{gam}} model)\cr
#' \tab \code{\link{fregre.gkam}}: Functional Generalized Kernel Additive Regression (an extension of  \code{\link{fregre.np}} model) \cr 
#' }
#' 
#' C.4. Functional response model (\code{\link{fregre.basis.fr}}) allows the
#' estimation of functional regression models with a functional response and a
#' single functional explicative covariate.\cr
#' 
#' C.5. \code{\link{fregre.gls}} fits functional linear model using generalized
#' least squares.  \code{\link{fregre.igls}} fits iteratively a functional
#' linear model using generalized least squares.  \cr
#' 
#' C.6. \code{\link{fregre.gsam.vs}}, Variable Selection using Functional Additive Models \cr
#' 
#' D.- Functional Supervised Classification \cr This section allows the
#' estimation of the groups in a training set of functional data \code{fdata}
#' class by different nonparametric methods of supervised classification. Once
#' these classifiers have been trained, they can be used to predict on new
#' functional data.\cr \cr Package allows the estimation of the groups in a
#' training set of functional data by different methods of supervised
#' classification. \cr \cr
#' 
#' D.1 Univariate predictor (x,y arguments, fdata class)
#' \tabular{ll}{ \tab \code{\link{classif.knn}} \cr \tab
#' \code{\link{classif.kernel}} \cr  }
#' 
#' D.2 Multiple predictors (formula,data arguments, ldata class)
#' \tabular{ll}{ \tab \code{\link{classif.glm}} \cr \tab
#' \code{\link{classif.gsam}} \cr \tab \code{\link{classif.gkam}} \cr  }
#' 
#' D.3 Depth classifiers (fdata or ldata class)
#' \tabular{ll}{ \tab \code{\link{classif.DD}} \cr \tab \code{\link{classif.depth}} \cr  }
#' 
#' D.4 Functional Classification usign k-fold CV 
#' \tabular{ll}{ \tab \code{\link{classif.kfold}} \cr }
#' 
#' E.- Functional Non-Supervised Classification \cr This section allows the
#' estimation of the groups in a functional data set \code{fdata} class by
#' kmeans method. \cr \tabular{ll}{ \tab \code{\link{kmeans.fd}} \cr }
#' 
#' F.- Functional ANOVA \cr \tabular{ll}{ \tab \code{\link{fanova.onefactor}}
#' \cr \tab \code{\link{fanova.RPm}} \cr \tab \code{\link{fanova.hetero}} \cr }
#' 
#' G.- Utilities and auxiliary functions:\cr \tabular{ll}{ \tab
#' \code{\link{fdata.bootstrap}} \cr \tab \code{\link{fdata2fd}} \cr \tab
#' \code{\link{fdata2pc}} \cr \tab \code{\link{fdata2pls}} \cr \tab
#' \code{\link{summary.fdata.comp}} \cr \tab \code{\link{cond.F}} \cr \tab
#' \code{\link{cond.quantile}} \cr \tab \code{\link{cond.mode}} \cr \tab
#' \code{\link{FDR}} \cr \tab \code{\link{Kernel}} \cr \tab
#' \code{\link{Kernel.asymmetric}} \cr \tab \code{\link{Kernel.integrate}} \cr
#' \tab \code{\link{metric.lp}} \cr \tab \code{\link{metric.kl}} \cr 
#' \tab \code{\link{metric.DTW}} \cr \tab \code{\link{metric.hausdorff}} \cr 
#' \tab \code{\link{metric.dist}} \cr \tab \code{\link{semimetric.NPFDA}} \cr 
#' \tab \code{\link{semimetric.basis}} \cr }
#' 
#' \tabular{ll}{ Package: \tab fda.usc\cr Type: \tab Package\cr Version: \tab
#' 2.0.3\cr Date: \tab 2021-06-03\cr License: \tab GPL-2 \cr LazyLoad: \tab
#' yes\cr \url{https://github.com/moviedo5/fda.usc/} }
#' 
#' @name fda.usc-package
#' @aliases fda.usc-package fda.usc
#' @docType package
#' @author \emph{Authors:} Manuel Febrero Bande \email{manuel.febrero@@usc.es}
#' and Manuel Oviedo de la Fuente \email{manuel.oviedo@@udc.es}
#' 
#' \emph{Contributors:} Pedro Galeano, Alicia Nieto-Reyes, Eduardo
#' Garcia-Portugues \email{eduardo.garcia@@usc.es} and STAPH group
#' \url{https://www.math.univ-toulouse.fr/~ferraty/} 
#' 
#' \emph{Maintainer:} Manuel Oviedo de la Fuente \email{manuel.oviedo@@udc.es}
#' @references Febrero-Bande, M., Oviedo de la Fuente, M. (2012).
#' \emph{Statistical Computing in Functional Data Analysis: The R Package
#' fda.usc.} Journal of Statistical Software, 51(4), 1-28.
#' \doi{10.18637/jss.v051.i04}
#' @keywords package
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