sphere.boot.bw {HDiR}

Spherical smoothing parameter for HDRs estimation

Description

This function provides the specific smoothing parameter for spherical HDRs estimation proposed in Saavedra-Nieves and Crujeiras (2021).

Usage

sphere.boot.bw(sample,bw="none",tau=0.5,ngrid=500,
               B=50,nborder=500,upper=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.

bw

Pilot 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). Default bw="none".

tau

Numeric probability. According to Saavedra-Nieves and Crujeiras (2021), 1-tau represents the probability coverage required for HDR. Default tau=0.5.

ngrid

Resolution of the density calculation. Default ngrid=500.

B

Integer string indicating the number of bootstrap resamples. Default B=50.

nborder

Maximum number of HDRs boundary points to be represented. Default nborder=500.

upper

Numerical upper value for bounding the optimization procedure. Default upper=NULL. In this case, the upper bound is equal to 1.5bw.

Details

Saavedra-Nieves and Crujeiras (2021) propose a specific smoothing parameter for HDRs estimation based on the minimization of the Hausdorff distance between the boundaries of the theoretical HDR and the plug-in estimator.

Value

A numeric value corresponding to the selected smoothing parameter.

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.
Saavedra-Nieves, P. and Crujeiras, R. M. (2021). Nonparametric estimation of directional highest density regions. Advances in Data Analysis and Classification, 1-36.

Examples

# HDR selector from a sample of size 1000 of model 4 in library HDiR
set.seed(1)
sample=rspheremix(500,model=4)
sphere.boot.bw(sample,tau=0.8,B=2)