kde_dir {DirStats}

Directional kernel density estimator

Description

Kernel density estimation with directional data as in the estimator of Bai et al. (1988).

Usage

kde_dir(x, data, h, L = NULL)

c_h(h, q, L = NULL)

lambda_L(L = NULL, q)

b_L(L = NULL, q)

d_L(L = NULL, q)

Arguments

x

evaluation points, a matrix of size c(nx, q + 1).

data

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

h

bandwidth, a scalar for kde_dir. Can be a vector for c_h.

L

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

q

dimension of S^q, q\ge 1.

Details

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

Value

kde_dir returns a vector of size nx with the evaluated kernel density estimator. c_h returns the normalizing constant for the kernel, a vector of length length(h). lambda_L, b_L, and d_L return moments of L.

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

Examples

# Sample
n <- 50
q <- 3
samp <- rotasym::r_vMF(n = n, mu = c(1, rep(0, q)), kappa = 2)

# Evaluation points
x <- rbind(diag(1, nrow = q + 1), diag(-1, nrow = q + 1))

# kde_dir
kde_dir(x = x, data = samp, h = 0.5, L = NULL)
kde_dir(x = x, data = samp, h = 0.5, L = function(x) exp(-x))

# c_h
c_h(h = 0.5, q = q, L = NULL)
c_h(h = 0.5, q = q, L = function(x) exp(-x))

# b_L
b_L(L = NULL, q = q)
b_L(L = function(x) exp(-x), q = q)

# d_L
d_L(L = NULL, q = q)
d_L(L = function(x) exp(-x), q = q)

# lambda_L
lambda_L(L = NULL, q = q)
lambda_L(L = function(x) exp(-x), q = q)