pgKDEsphere (version 1.0.2)

pi.kappa: 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)

Value

A numerical value with the selected data-driven smoothing parameter.

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.

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)