Bootstrap BCa Quantiles of the quantile function Let's say I have a vector $x$ on $n=250,$
(in R)
x = rnorm(250)

The quantile of $\alpha=0.01$ is :

quantile(x,0.01)
       1% 
-2.700463 

Now is that theoretically right to estimate the bootstrap quantiles of the quantile function at any confidence level ? For example I am using the BCa method described by Efron in his book:
# setting the function to estimate 
theta1 = function(x){  
 ql = quantile(x,0.01)
 return(ql)
}
# bootstrap the data with BCa method 
bca = bootstrap::bcanon(x,5000,theta1,alpha=c(0.01,(1-0.01)))
# extract the two quantiles of the function
bca$confpoints

Resulting to :
     alpha bca point
[1,]  0.01 -3.086066
[2,]  0.99 -2.192914


Now, what I have took, I think, is the upper(0.99) and lower(0.01) bootstrap quantiles of the quantile function at level $alpha=0.01$.
Question 1) Am I right in the last phrase? Do I interpret correctly the output?
Question 2) Am I theoretically allowed to do so ?

The endpoints of a confidence interval are quantiles of the sampling distribution of the statistic.
So yes theoritically these are the 0.01- and 0.99-quantiles of the sampling distribution of the 0.01-quantile of a standard normal distribution. But isn't this a mouthful? Why not say this is a 98% two-sided confidence interval for the 0.01-quantile of the standard normal?
