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).
bw.rt(x, robust=FALSE, alpha=0.5)Value of the smoothing parameter.
Data from which the smoothing parameter is to be computed. The object is coerced to class circular.
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.
Arc probability when robust=TRUE. Default is alpha=0.5. See Details.
Maria Oliveira, Rosa M. Crujeiras and Alberto Rodriguez--Casal
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).
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/
kern.den.circ, bw.CV, bw.pi, bw.boot
set.seed(2012)
n <- 100
x <- rcircmix(n,model=7)
bw.rt(x)
bw.rt(x, robust=TRUE)
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