egarpor / DirStats

Nonparametric kernel density estimation, bandwidth selection, and other utilities for analyzing directional data

DirStats

Overview

Currently implementing nonparametric kernel density estimation, bandwidth selection, and other utilities for analyzing directional data. Further nonparametric tools expected to be included in subsequent releases.

Installation

Get the released version from CRAN:

# Install the package
install.packages("DirStats")

# Load package
library(DirStats)

Alternatively, get the latest version from GitHub:

# Install the package
library(devtools)
install_github("egarpor/DirStats")

# Load package
library(DirStats)

Usage

The following are examples of the usage of the Bai et al. (1988)’s kernel density estimator, the cross-validatory bandwidth selectors in Hall et al. (1987), and the plug-in bandwidth selectors in García-Portugués (2013).

Compute bandwidths

# Sample from a von Mises--Fisher on S^2
q <- 2
n <- 300
set.seed(42)
samp <- rbind(rotasym::r_vMF(n = n / 3, mu = c(rep(0, q), 1), kappa = 5),
              rotasym::r_vMF(n = n / 3, mu = c(rep(0, q), -1), kappa = 5),
              rotasym::r_vMF(n = n / 3, mu = c(1, rep(0, q)), kappa = 5))

# LCV bandwidth
(h_LCV <- bw_dir_lcv(data = samp)$h_opt)
#> [1] 0.2567438

# LSCV bandwidth
(h_LSCV <- bw_dir_lscv(data = samp)$h_opt)
#> [1] 0.232965

# ROT bandwidth
(h_ROT <- bw_dir_rot(data = samp))
#> [1] 0.4053648

# Mixture fit, for AMI and EMI bandwidth selectors
fit_mix <- bic_vmf_mix(data = samp)

# AMI bandwidth
(h_AMI <- bw_dir_ami(data = samp, fit_mix = fit_mix))
#> [1] 0.2054242

# EMI bandwidth
(h_EMI <- bw_dir_emi(data = samp, fit_mix = fit_mix)$h_opt)
#> [1] 0.22527

Compute kernel density estimator

# Compute kde
l <- 200
th <- seq(0, 2 * pi, l = l)
phi <- seq(0, pi, l = l / 2)
ang <- expand.grid(th = th, phi = phi)
x <- to_sph(th = ang$th, ph = ang$phi)
kde <- kde_dir(x = x, data = samp, h = h_EMI)

# Visualization
contour(x = th, y = phi, z = matrix(kde, nrow = l, ncol = l / 2),
        col = viridisLite::viridis(15), 
        levels = round(seq(min(kde), max(kde), length.out = 15), 4), 
        lwd = 2, xlab = expression(theta), ylab = expression(phi))
points(to_rad(samp), pch = 16)

References

Bai, Z. D., Rao, C. R., and Zhao, L. C. (1988). Kernel estimators of density function of directional data. Journal of Multivariate Analysis, 27(1):24–39. doi:10.1016/0047-259X(88)90113-3.

García-Portugués, E. (2013). Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electronic Journal of Statistics, 7:1655–1685. doi:10.1214/13-ejs821.

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.