First cumulative survival estimator (4.8)

V_{1,h}(x, y) = int_x^Inf g'(z) V((z - y)/h) dz. This variant is built so that d/dt of the cumulative survival is exactly minus the survival estimator – the structural identity of the population quantities is preserved by the estimators. morie_fauzi_cumulative_survival_2() is the mirror construction and does not preserve it; the two differ in bias coefficient (b_2 here, b_3 there) and share the same covariance.

Usage

morie_fauzi_cumulative_survival_1(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 (TRUE), bias_coefficient, mirror_note, n, method.

References

Fauzi and Maesono (2023), Eq. (4.8), (4.9), (4.15).

Examples

set.seed(1)
morie_fauzi_cumulative_survival_1(stats::rexp(100), c(0.5, 1))$S_survival
#> [1] 0.6540805 0.3902929