The mirror of (4.8): V_{2,h}(x, y) = int_{-Inf}^y g'(z) V((x - z)/h) dz.
Multiplying V by g' is what makes this an estimator of the
cumulative survival function at all. It does NOT preserve the
derivative relation that morie_fauzi_cumulative_survival_1()
does, and its bias carries b_3 rather than b_2; the covariance
is the same.
Usage
morie_fauzi_cumulative_survival_2(x, t_grid, h = NULL, transform = "log")
Arguments
- x
numeric sample strictly inside the support.
- t_grid
evaluation points strictly inside the support.
- h
bandwidth on the transformed scale.
- transform
"log" or "identity".
Value
list: t_grid, S_cumulative, S_survival, bandwidth,
preserves_derivative_relation (FALSE), bias_coefficient,
g_prime_note, same_covariance_as_first, n, method.
References
Fauzi and Maesono (2023), Eq. (4.17), (4.18), (4.21).
Examples
set.seed(1)
morie_fauzi_cumulative_survival_2(stats::rexp(60), c(0.5, 1))$S_cumulative
#> [1] 0.5583345 0.3139212
