Boundary-free mean-residual-life estimator (4.24)

m~_{X,2}(t) – the ratio of the second cumulative survival estimator to the survival estimator. Bias is O(h^2) everywhere including the boundary, with the Theorem 4.3 constant h^2/(2 S_X(t)) [b_3(t) + m_X(t) b_1(t)] int y^2 K(y) dy.

Usage

morie_fauzi_mrl_boundary_free_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, mrl, bandwidth, bias_order, bias_formula, variance_vanishes_at_boundary, prefer_variant_1_when, n, method.

Details

Prefer the variant built on morie_fauzi_cumulative_survival_1() when the analytic relation between S and the cumulative survival must be preserved (Remark 4.2).

References

Fauzi and Maesono (2023), Eq. (4.24), Theorem 4.3. Transcribed from the PDF, where (4.24) is printed in full.

Examples

set.seed(1)
morie_fauzi_mrl_boundary_free_2(stats::rexp(60), c(0.5, 1))$mrl
#> [1] 0.8373598 0.8401206