Order-m kernel and its moments

Moments 1..m-1 vanish, pushing the bias to O(h^m). A non-negative function cannot have a vanishing second moment, so orders above 2 necessarily take NEGATIVE values – the density can go negative and the distribution non-monotone. Acceptable for quantiles, where the estimand is a location; not for a density to be plotted.

Usage

morie_fauzi_order_m_kernel(u, m = 4L)

Arguments

u

evaluation points.

m

kernel order: 2, 4 or 6.

Value

list: u, K, order, moments, takes_negative_values, bias_order, tradeoff, method.

References

Fauzi and Maesono (2023), Ch. 3; Mueller (1991).

Examples

morie_fauzi_order_m_kernel(c(0, 1, 2), m = 4)$K
#> [1]  0.59841342  0.24197072 -0.02699548