\((F + t_n h_n)(\xi - \epsilon) \le p \le (F + t_n h_n)(\xi)\).
The two-sided bracket is what makes a monotone inverse
differentiable. Mirrors morie.fn.ksr043.
Usage
morie_quantile_hadamard(F, h_n, t_n, p, eps_pn = NULL)
Arguments
- F
base CDF.
- h_n
perturbation direction.
- t_n
scale.
- p
quantile level in (0, 1).
- eps_pn
optional left offset.
Value
list: lower, upper, xi_perturbed, sandwich_holds.
References
Kosorok (2008), Ch. 2.
Examples
morie_quantile_hadamard(stats::pnorm, function(z) 0.1 * stats::dnorm(z),
0.01, 0.7)$sandwich_holds
#> [1] TRUE
