b_1(t) = g''(g^{-1}(t)) f_X(t) + g'(g^{-1}(t))^2 f_X'(t). The
transformation does not remove the bias of a boundary-free
estimator; it makes the constant computable and keeps the order at
O(h^2) right up to the edge.
Usage
morie_fauzi_b1_coefficient(
t,
f_X,
f_X_prime = NULL,
S_X = NULL,
transform = "log"
)
Arguments
- t
evaluation points strictly inside the support.
- f_X
density at t.
- f_X_prime
density derivative at t; required here.
- S_X
survival at t; unused by b_1, kept for signature
parity with the b_2 and b_3 companions.
- transform
"log" or "identity".
Value
list: t, b_1, g_prime, g_double_prime, bias_order,
contrast, transform, method.
References
Fauzi and Maesono (2023), Eq. (4.14).
Examples
morie_fauzi_b1_coefficient(1, f_X = 0.5, f_X_prime = -0.5)$b_1
#> [1] 0
