Estimates on the transformed scale, where a symmetric kernel is
legitimate because the support is unbounded, then maps back:
f~_X(t) = 1/(n h g'(g^{-1}(t))) sum K((g^{-1}(t) - g^{-1}(X_i))/h).
Usage
morie_fauzi_boundary_free_kde(x, grid = NULL, h = NULL, transform = "log")
Arguments
- x
numeric sample strictly inside the support.
- grid
evaluation points strictly inside the support.
- h
bandwidth on the transformed scale.
- transform
"log" or "identity".
Value
list: grid, density, bandwidth, transform, jacobian
(= 1/g'(g^{-1}(t))), g_prime, mass, boundary_bias_order,
jacobian_note, n, method.
Details
The factor 1/g'(g^{-1}(t)) is mandatory. Without it the result
is a density on the transformed scale, not the original one. (The
distilled text file in the reference library omits it; the PDF
does not.)
References
Fauzi and Maesono (2023), Ch. 4. Transcribed from the PDF.
Examples
set.seed(1)
morie_fauzi_boundary_free_kde(stats::rexp(300), grid = c(0.1, 1))$density
#> [1] 0.7861862 0.3964652
