circ.boot.bw {HDiR}

Circular smoothing parameter for HDRs estimation

Description

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

Usage

circ.boot.bw(sample, bw = bw.CV(circular(sample),
upper=100), tau = 0.5, B = 50, upper = 1.5 * bw)

Arguments

sample

Numeric vector of angles in radians.

bw

Pilot soothing parameter to be used. Following Oliveira et al. (2014), the value of the smoothing parameter can be chosen by using the functions bw.rt, bw.CV, bw.pi or bw.boot. Default bw=bw.CV providing a cross-validation bandwidth.

tau

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

B

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

upper

Numerical upper value for bounding the optimization procedure. Default 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

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 500 of model 5 in NPCirc
library(NPCirc)
set.seed(1)
sample<- rcircmix(500, model=5)
circ.boot.bw(sample,tau=0.4,B=2)