p(1-p)/(n f(Q(p))^2), equivalently Q'(p)^2 p(1-p)/n since
Q' = 1/f(Q). As p approaches 0 or 1 the binomial part shrinks,
which suggests extreme quantiles are easier – they are not, since
the density part grows faster for thinning tails.
Usage
morie_fauzi_quantile_amse(p, n, f_at_quantile = NULL, Q_prime = NULL)
Arguments
- p
probability levels strictly in (0, 1).
- n
sample size.
- f_at_quantile
density at Q(p); supply this or Q_prime.
- Q_prime
the quantile-function derivative at p.
Value
list: p, amse, se, binomial_part, density_part, n,
tail_note, method.
References
Fauzi and Maesono (2023), Eq. (3.3).
Examples
morie_fauzi_quantile_amse(0.5, 500, f_at_quantile = 0.5)$amse
#> [1] 0.002
