# bw.rt: Rule of thumb In NPCirc: Nonparametric Circular Methods

## 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

 1 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 κ 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 κ is estimated as follows:

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

2. Obtain the estimated \hatκ 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.

## Value

Value of the smoothing parameter.

## Author(s)

Mar?a Oliveira, Rosa M. Crujeiras and Alberto Rodr?guez–Casal

## References

Oliveira, M., Crujeiras, R.M. and Rodr?guez–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 Rodr?guez–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 Rodr?guez–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/

kern.den.circ, bw.CV, bw.pi, bw.boot
 1 2 3 4 5 set.seed(2012) n <- 100 x <- rcircmix(n,model=7) bw.rt(x) bw.rt(x, robust=TRUE)