sphere.scatterplot {HDiR}

Spherical scatterplot for plug-in HDRs

Description

This function produces a spherical scatterplot with points coloured according to the HDRs in which they fall.

Usage

sphere.scatterplot(sample,tau=c(0.25,0.5,.75),bw="none",
                   ngrid=500,nborder=1000,tol=0.1, col=NULL)

Arguments

sample

A matrix whose rows represent points on the unit sphere in Cartesian coordinates. If a row norm is different from one, a message appears indicating that they must be standardized.

tau

Numeric vector of probabilities. According to Saavedra-Nieves and Crujeiras (2021), 1-tau represents the probability coverages required for HDRs.

bw

Smoothing parameter to be used. According to Directional package, this can be either "none" for cross validation or "rot" for the rule of thumb suggested by García-Portugués (2013). It could be also selecting by considering sphere.boot.bw, the new smoothing parameter proposed in Saavedra-Nieves and Crujeiras (2021). Default bw="none".

ngrid

Sets the resolution of the density calculation. Default ngrid=500.

nborder

Maximum number of HDRs boundary points to be represented. Default nborder= 1000.

tol

Tolerance parameter to determinate the boundary of HDRs. Default tol=0.1.

col

Vector containing the color numbers for plotting the scatterplot. If NULL, a default color palette is used.

Details

A detailed definition of directional HDRs and of their plug-in estimators is given in Saavedra-Nieves and Crujeiras (2021).
Package Directional is used to compute tha von Mises-Fisher kernel density estimate.
The density quantile algorithm proposed in Hyndman (1996) is used to calculate the threshold of HDR.
The scatterplot is created colouring the sample points according to which HDR they fall.

Value

A scatterplot showing the points coloured according to which HDR they fall. Futhermore, a list where the number of components is equal to the number HDR estimated or, equivalently, to the length of tau vector. Each component contains the sample points in each HDR from the smallest value of tau to the biggest one.

Author(s)

Paula Saavedra-Nieves and Rosa M. Crujeiras.

References

García-Portugués, E. (2013). Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electronic Journal of Statistics, 7, 1655-1685.
Tsagris, M., Athineou, G., Sajib, A., Tsagris, M. M. and Imports, M. A. S. S. (2016). Package Directional. https://cran.r-project.org/package=Directional.
Saavedra-Nieves, P. and Crujeiras, R. M. (2021). Nonparametric estimation of directional highest density regions. Advances in Data Analysis and Classification, 1-36.

Examples

# Scatterplot of model 4 in library HDiR
set.seed(1)
sample=rspheremix(1000,model=4)
sphere.scatterplot(sample,tau=c(.2,.5,.8))
#Scatterplot of model 9 in library HDiR
set.seed(1)
sample=rspheremix(1000,model=9)
sphere.scatterplot(sample)