The gamma kernel's support IS [0, Inf), so no mass ever lands on
the negative half-line and the boundary bias simply does not
arise: the estimator is consistent at zero, where a
Gaussian-kernel estimate is not. modified = TRUE applies Fauzi's
self-elimination correction, which cancels the leading bias term.
Usage
morie_fauzi_gamma_kde(x, grid = NULL, h = NULL, modified = FALSE, a = 2)
Arguments
- x
non-negative numeric sample.
- grid
evaluation points in [0, Inf); data-driven if NULL.
- h
bandwidth; sd(x) * n^{-2/5} if NULL.
- modified
apply the self-elimination correction.
- a
the correction's second-bandwidth multiplier, not 1.
Value
list: grid, density, bandwidth, modified, a,
boundary_consistent (TRUE), bias_order, mass, why_it_works, n,
method.
References
Fauzi and Maesono (2023), Ch. 1; Chen (1999).
Examples
set.seed(1)
morie_fauzi_gamma_kde(stats::rexp(200), grid = c(0, 1), h = 0.1)$density
#> [1] 0.6273707 0.4098218
