| Type: | Package |
| Title: | Parametrically Guided Kernel Density Estimator for Spherical Data |
| Version: | 1.0.1 |
| Date: | 2024-02-06 |
| Author: | María Alonso-Pena [aut, cre], Gerda Claeskens [aut], Irène Gijbels [aut] |
| Maintainer: | María Alonso-Pena <maria.alonsopena@ugr.es> |
| Description: | Nonparametric density estimation for (hyper)spherical data by means of a parametrically guided kernel estimator (adaptation of the method of Hjort and Glad (1995) <doi:10.1214/aos/1176324627> to the spherical setting). The package also allows the data-driven selection of the smoothing parameter and the representation of the estimated density for circular and spherical data. Estimators of the density without guide can also be obtained. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | Rcpp (≥ 1.0.11), rgl, Directional, DirStats, circular, matrixStats, rotasym, movMF |
| LinkingTo: | Rcpp, RcppArmadillo |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | yes |
| Packaged: | 2024-02-06 14:07:55 UTC; Despacho 7 |
| Repository: | CRAN |
| Date/Publication: | 2024-02-07 17:50:07 UTC |
Internal pgKDEsphere Functions
Description
Internal pgKDEsphere functions.
Details
These are not to be called by the user.
Value
No return value, called for side effects.
pi.kappa
Description
Function pi.kappa computes a plug-in type smoothing parameter for the parametrically guided (hyper)spherical kernel density estimator, equipped with a von Mises-Fisher guide.
Usage
pi.kappa(datax, mu0, tau0, guide = TRUE)
Arguments
datax |
Matrix containing the data in cartesian coordinates, where the number of rows is the number of observations and the number of columns is the dimension of the Euclidean space where the sphere is embebed. |
mu0 |
Vector containing the mean direction of the von Mises-Fisher guide. |
tau0 |
Numerical value containing the concentration of the von Mises-Fisher guide. |
guide |
Logical; if TRUE, the estimator with a von Mises-Fisher as guide is computed. If FALSE, the classical kernel density estimator without guide is computed (equivalent to uniform guide). |
Details
See Alonso-Pena et al. (2023) for details.
Value
A numerical value with the selected data-driven smoothing parameter.
References
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
Examples
library(Directional)
library(movMF)
# Data generation
n<-200
mu<-matrix(c(0,0,1,0,0,-1),ncol=3,byrow=TRUE)
k<-c(7,2)
probs<-c(0.85,0.15)
datax<-rmovMF(n,k*mu,alpha=probs)
# Estimation of parameters of a vMF
param<-vmf.mle(datax)
mu0<-param$mu
tau0<-param$kappa
# Selection of the smoothing parameter
kappa <- pi.kappa(datax,mu0,tau0)
sphkde.pg
Description
Function sphkde.pg computes the kernel density estimator for (hyper)spherical data with a parametric guide, which corresponds to the von Mises-Fisher model.
Usage
sphkde.pg(datax, kappa = NULL, eval.points = NULL, guide = TRUE)
Arguments
datax |
Matrix containing the data in cartesian coordinates, where the number of rows is the number of observations and the number of columns is the dimension of the Euclidean space where the sphere is embebed. |
kappa |
Smoothing parameter. It refers to the concentration when employing a von Mises-Fisher kernel. |
eval.points |
Matrix containing the evaluation points for the estimation of the density. |
guide |
Logical; if TRUE, the estimator with a von Mises-Fisher as guide is computed. If FALSE, the classical kernel density estimator without guide is computed (equivalent to uniform guide). |
Details
See Alonso-Pena et al. (2023) for details.
Value
An object with class "sphkde" whose underlying structure is a list containing the following components:
estim |
The estimated values of the density. |
kappa |
The smoothing parameter used. |
data |
The n coordinates of the points where the regression is estimated. |
eval.points |
The points where the estimated density was evaluated. |
data |
Original dataset. |
References
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
Examples
library(movMF)
n<-200
mu<-matrix(c(0,0,1,0,0,-1),ncol=3,byrow=TRUE)
k<-c(7,2)
probs<-c(0.85,0.15)
datax<-rmovMF(n,k*mu,alpha=probs)
est<-sphkde.pg(datax,guide=TRUE)
sphkde.plot(est,type="sph")
sphkde.plot
Description
Function sphkde.plot provides a graphical representation of the parametrically guided kernel density estimator for spherical and circular data. For circular data, both linear and circular representations are available. For spherical data, an interactive 3D spherical representation is provided.
Usage
sphkde.plot(object, type = "sph", axis = TRUE, shrink = 1.2)
Arguments
object |
Object of the class |
type |
Character string giving the desired type of plot. For circular data, it can be "sph" for a circular representation or "line" for a linear representation. For spherical data the value "sph" is required. |
axis |
Logical; if TRUE, the axis are represented in the spherical representation. If FALSE, axis are not represented. Only for spherical representations. |
shrink |
Numeric parameter that controls the size of the plotted circle in the circular representations. Default is 1.3. Larger values shrink the circle, while smaller values enlarge the circle. |
Details
See Alonso-Pena et al. (2023) for details.
Value
sphkde.plot is called for the side effect of drawing the plot.
References
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
Examples
library(movMF)
n<-200
mu<-matrix(c(0,0,1,0,0,-1),ncol=3,byrow=TRUE)
k<-c(7,2)
probs<-c(0.85,0.15)
datax<-rmovMF(n,k*mu,alpha=probs)
est<-sphkde.pg(datax,guide=TRUE)
sphkde.plot(est,type="sph")