bw.boot {NPCirc}

Bootstrap method

Description

This function implements the bootstrap procedure proposed by Di Marzio et al. (2011) for selecting the smoothing parameter for density estimation taking the von Mises density as kernel.

Usage

bw.boot(x, lower=0, upper=100, np=500, tol=0.1)

Arguments

x

Data from which the smoothing parameter is to be computed. The object is coerced to class circular.

lower, upper

lower and upper boundary of the interval to be used in the search for the value of the smoothing parameter. Default lower=0 and upper=100.

np

Number of points where to evaluate the estimator for numerical integration. Default np=500.

tol

Convergence tolerance for optimize.

Details

This method is based on the proposal of Taylor (1989) for linear data. See also Oliveira et al. (2012). The NAs will be automatically removed.

Value

Value of the smoothing parameter.

Author(s)

Maria Oliveira, Rosa M. Crujeiras and Alberto Rodriguez–Casal

References

Di Marzio, M., Panzera A. and Taylor, C.C. (2011) Kernel density estimation on the torus. Journal of Statistical Planning and Inference, 141, 2156–2173.

Oliveira, M., Crujeiras, R.M. and Rodriguez–Casal, A. (2012) A plug–in rule for bandwidth selection in circular density. Computational Statistics and Data Analysis, 56, 3898–3908.

Taylor, C.C. (1989) Bootstrap choice of the smoothing parameter in kernel density estimation. Biometrika, 76, 705–712.

Oliveira, M., Crujeiras R.M. and Rodriguez–Casal, A. (2014) NPCirc: an R package for nonparametric circular methods. Journal of Statistical Software, 61(9), 1–26. https://www.jstatsoft.org/v61/i09/

See Also

kern.den.circ, bw.rt, bw.CV, bw.pi

Examples

set.seed(2012)
n <- 100
x <- rcircmix(n, model=17)
bw.boot(x, lower=0, upper=20)