| Title: | Parametrically Guided Kernel Density Estimator for Spherical Data |
|---|---|
| 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. |
| Authors: | María Alonso-Pena [aut, cre], Gerda Claeskens [aut], Irène Gijbels [aut] |
| Maintainer: | María Alonso-Pena <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.1 |
| Built: | 2024-11-04 06:44:30 UTC |
| Source: | CRAN |
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.
pi.kappa(datax, mu0, tau0, guide = TRUE)pi.kappa(datax, mu0, tau0, guide = TRUE)
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). |
See Alonso-Pena et al. (2023) for details.
A numerical value with the selected data-driven smoothing parameter.
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
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)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)
Function sphkde.pg computes the kernel density estimator for (hyper)spherical data with a parametric guide, which corresponds to the von Mises-Fisher model.
sphkde.pg(datax, kappa = NULL, eval.points = NULL, guide = TRUE)sphkde.pg(datax, kappa = NULL, eval.points = NULL, guide = TRUE)
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). |
See Alonso-Pena et al. (2023) for details.
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. |
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
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")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")
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.
sphkde.plot(object, type = "sph", axis = TRUE, shrink = 1.2)sphkde.plot(object, type = "sph", axis = TRUE, shrink = 1.2)
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. |
See Alonso-Pena et al. (2023) for details.
sphkde.plot is called for the side effect of drawing the plot.
Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2023) Nonparametric estimation of densities on the hypersphere using a parametric guide. Under review.
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")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")