Bootstrap Percentile Confidence Interval

(Compared to the Bootstrap-t Confidence Interval, I like this one better because it is easier to understand and compute and it is faster too)

We can directly find the quantile $\alpha/2$-th and $(1-\alpha/2)$-th from the bootstrap replicates.

\[(\hat{\theta_B}^{\alpha/2}, \hat{\theta_B}^{(1-\alpha/2)})\]

For example, the bootstrap percentile confidence interval of the skewness of the forearm data is

load forearm;
theta = skewness(forearm);
n=length(forearm);
B=1000;
bootstat=bootstrp(B,'skewness',forearm);
alpha=0.05;
k=B*alpha/2;
szvals=sort(bootstat);
blo = szvals(k);
bhi = szvals(B-k);
[blo,bhi]

ans =

   -0.3940    0.1794

Efron and Tibshirani (1993) stated that this method is more stable and better theoretical coverage properties than the bootstrap-t.