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

Source: R/K(mi).R
K_mi.Rd

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

Usage

K_mi(mi)

Arguments

mi

A single numeric value greater than 0.5. In package estimators, mi corresponds to one component of the integer shift vector m.

Value

A positive numeric scalar.

Details

The implemented formula is $$ K(m_i) = \sqrt{\frac{1}{6} + \frac{1}{12m_i^2}} + \frac{4m_i^2 - 1}{6\sqrt{2}m_i} \log\left( \frac{\sqrt{3} + \sqrt{4m_i^2 + 2}}{\sqrt{4m_i^2 - 1}} \right). $$

See also

compute_bi_optim(), G_i(), compute_G_star()

Examples

K_mi(1)
#> [1] 0.8116126
K_mi(2)
#> [1] 0.8161827