| quantONE {emplikAUC} | R Documentation |
Smoothed quantile estimation from the given x-sample.
Description
This function computes the smoothed quantile estimate,
using the smoothing function smooth3. (or it can be changed easily)
Otherwise it is similar to R function quantile().
Compare to quantile(x, prob, type=9).
myeps is a scalar, must > 0. It is the smoothing window width.
Usage
quantONE(x, prob, myeps=(length(x))^(-0.75))
Arguments
x |
a vector of observations, length m, the sample. |
prob |
a probabilty. |
myeps |
The smoothing window width, must >0. |
Details
This function is called by myEstPaucT.
It is listed here because the user may find it useful elsewhere.
Known problems: when the input prob is too close to 0 or 1 (distance less than 0.03),
the computation will stop.
Also, if the solution to the equation
\tau ~| ~~~ \frac{1}{m} \sum_{i=1}^m smooth3vec(X_i, \tau, myeps) = prob
is not unique, this function only returns one of the solutions.
Value
The function quantONE returns a scalar that is the estimated (prob)-th quantile of X distribution.
Author(s)
Mai Zhou <maizhou@gmail.com>.
References
Zhao, Y., Ding, X. and Zhou (2021). Confidence Intervals of AUC and pAUC by Empirical Likelihood. Tech Report. https://www.ms.uky.edu/~mai/research/eAUC1.pdf
Examples
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
#### To estimate the 70-th percentile of x distrubution:
quantONE(x=x, prob=0.7)
#### we should get 239.9474.