This function provides a least squares cross-validation smoothing parameter or a likelihood cross-validation smoothing parameter for density estimation.
bw.CV(x, method="LCV", lower=0, upper=50, tol=1e-2, np=500)Value of the smoothing parameter.
Data from which the smoothing parameter is to be computed. The object is coerced to class circular.
Character string giving the cross-validation rule to be used. This must be one of "LCV" or "LSCV". Default method="LCV".
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=50.
Convergence tolerance for optimize. Default tol=1e-2.
Number of points where to evaluate the estimator for numerical integration when method="LSCV". Default np=500.
Maria Oliveira, Rosa M. Crujeiras and Alberto Rodriguez--Casal
The LCV smoothing parameter is obtained as the value of \(\nu\) that maximizes the logarithm of the likelihood cross-validation function (8) in Oliveira et al. (2013). The LSCV smoothing parameter is obtained as the value of \(\nu\) that minimizes expression (7) in Oliveira et al. (2013). See also Hall et al. (1987) and Oliveira et al. (2012). The NAs will be automatically removed.
Hall, P., Watson, G.S. and Cabrera, J. (1987) Kernel density estimation with spherical data, Biometrika, 74, 751--762.
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.
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.rt, bw.pi, bw.boot
set.seed(2012)
n <- 100
x <- rcircmix(n, model=11)
bw.CV(x, method="LCV", lower=0, upper=20)
bw.CV(x, method="LSCV", lower=0, upper=20)
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