bw_dir_cv {DirStats}

Cross-validation bandwidth selectors for directional data

Description

Likelihood and least squares cross-validation bandwidth selectors for kernel density estimation with directional data.

Usage

bw_dir_lcv(data, h_grid = exp(seq(log(0.05), log(1.5), l = 100)), L = NULL,
  plot_it = FALSE, optim = TRUE, optim_par = 0.25, optim_lower = 0.06,
  optim_upper = 10)

bw_dir_lscv(data, h_grid = exp(seq(log(0.05), log(1.5), l = 100)),
  L = NULL, plot_it = FALSE, optim = TRUE, R_code = FALSE,
  optim_par = 0.25, optim_lower = 0.06, optim_upper = 10)

Arguments

data

directional data, a matrix of size c(n, q + 1).

h_grid

vector of bandwidths for performing a grid search. Defaults to
exp(seq(log(0.05), log(1.5), l = 100)).

L

kernel function. Set internally to function(x) exp(-x) (von Mises–Fisher kernel) if NULL (default).

plot_it

display an informative plot on the optimization's grid search? Defaults to FALSE.

optim

run an optimization? Defaults to TRUE. Otherwise, a grid search on h is done. Only effective if L = NULL.

optim_par, optim_lower, optim_upper

parameters passed to par, lower, and upper in optim when using the "L-BFGS-B" method. Default to 0.25, 0.06 (to avoid numerical instabilities), and 10.

R_code

use slower R code when L = NULL? Defaults to FALSE.

Details

data is not checked to have unit norm, so the user must be careful. When L = NULL, faster FORTRAN code is employed.

bw_dir_lscv employs Monte Carlo integration for q > 2, which results in a random output. Use set.seed before to avoid it.

Value

A list with entries:

• h_opt: selected bandwidth.

• h_grid: h_grid, if used (otherwise NULL).

• CV_opt: minimum of the CV loss.

• CV_grid: value of the CV function at h_grid, if used (otherwise NULL).

Source

The function bw_dir_lscv employs Netlib's subroutine ribesl for evaluating the modified Bessel function of the first kind. The subroutine is based on a program by Sookne (1973) and was modified by W. J. Cody and L. Stoltz. An earlier version was published in Cody (1983).

References

Cody, W. J. (1983). Algorithm 597: Sequence of modified Bessel functions of the first kind. ACM Transactions on Mathematical Software, 9(2):242–245. doi:10.1145/357456.357462

Hall, P., Watson, G. S., and Cabrera, J. (1987). Kernel density estimation with spherical data. Biometrika, 74(4):751–762. doi:10.1093/biomet/74.4.751

Sookne, D. J. (1973). Bessel functions of real argument and integer order. Journal of Research of the National Bureau of Standards, 77B:125–132.

Examples

# Sample
n <- 25
q <- 2
set.seed(42)
samp <- rotasym::r_vMF(n = n, mu = c(1, rep(0, q)), kappa = 2)

# bw_dir_lcv
bw_dir_lcv(data = samp, optim = TRUE)$h_opt
bw_dir_lcv(data = samp, optim = FALSE, plot_it = TRUE)$h_opt
bw_dir_lcv(data = samp, L = function(x) exp(-x))$h_opt

# bw_dir_lscv
set.seed(42)
bw_dir_lscv(data = samp, optim = TRUE)$h_opt
bw_dir_lscv(data = samp, optim = FALSE, plot_it = TRUE)$h_opt
bw_dir_lscv(data = samp, optim = FALSE, R_code = TRUE)$h_opt
bw_dir_lscv(data = samp, L = function(x) exp(-x))$h_opt