Compute the \(G(m_i)\) bandwidth constant

Computes the scalar constant \(G(m_i)\) used by compute_bi_optim().

Usage

G_i(mi)

Arguments

mi

A single positive numeric value. In package estimators, mi corresponds to one component of the integer shift vector m.

Value

A positive numeric scalar.

Details

The implemented formula is $$G(m_i) = \frac{1}{12}\left(1 + \frac{1}{2m_i^2}\right).$$

See also

compute_bi_optim(), K_mi(), compute_G_star()

Examples

G_i(1)
#> [1] 0.125
G_i(2)
#> [1] 0.09375