bw.rt {NPCirc}

Rule of thumb

Description

This function implements the selector proposed by Taylor (2008) for density estimation, based on an estimation of the concentration parameter of a von Mises distribution. The concentration parameter can be estimated by maximum likelihood or by a robustified procedure as described in Oliveira et al. (2013).

Usage

bw.rt(x, robust=FALSE, alpha=0.5)

Arguments

x

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

robust

Logical, if robust=FALSE the parameter \kappa is estimated by maximum likelihood, if TRUE it is estimated as described in Oliveira et al. (2012b). Default robust=FALSE.

alpha

Arc probability when robust=TRUE. Default is alpha=0.5. See Details.

Details

When robust=TRUE, the parameter \kappa is estimated as follows:

1. Select \alpha \in (0, 1) and find the shortest arc containing \alpha \cdot 100\% of the sample data.

2. Obtain the estimated \hat\kappa in such way that the probability of a von Mises centered in the midpoint of the arc is alpha.

The NAs will be automatically removed.

See also Oliveira et al. (2012).

Value

Value of the smoothing parameter.

Author(s)

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

References

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.

Oliveira, M., Crujeiras R.M. and Rodriguez–Casal, A. (2013) Nonparametric circular methods for exploring environmental data. Environmental and Ecological Statistics, 20, 1–17.

Taylor, C.C. (2008) Automatic bandwidth selection for circular density estimation. Computational Statistics and Data Analysis, 52, 3493–3500.

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.CV, bw.pi, bw.boot

Examples

set.seed(2012)
n <- 100
x <- rcircmix(n,model=7)
bw.rt(x)
bw.rt(x, robust=TRUE)