Compute the \(G^*\) bandwidth constant

Computes the dimension-dependent constant \(G^*\) used by compute_bi_optim().

Usage

compute_G_star(d)

Arguments

d

A single positive integer giving the data dimension.

Value

A positive numeric scalar.

Details

The implemented formula is $$G^* = 2^{\frac{3(d - 4)}{2(4 + d)}} \exp\left(\frac{1}{4 + d}\right) \frac{\pi^{d / 2}}{4 + d}.$$

See also

compute_bi_optim(), G_i(), K_mi()

Examples

compute_G_star(1)
#> [1] 0.2320261
compute_G_star(2)
#> [1] 0.4373872