Bootstrap standard error from three replicates

Question

You bootstrap a small dataset to get a standard error for the 90th percentile of a loss distribution. As a bare-bones illustration you keep only three bootstrap replicates of that percentile:

$90, \quad 100, \quad 110.$

Estimate the bootstrap standard error of the 90th percentile.

Accepted Answer

The bootstrap standard error is the standard deviation of the replicate values (sample version, dividing by B - 1 = 2). Step 1, mean of the replicates. \bar{	heta}^ = \frac{90 + 100 + 110}{3} = \frac{300}{3} = 100. Step 2, squared deviations from 100. (-10)^2 + 0^2 + (10)^2 = 100 + 0 + 100 = 200. Step 3, divide by B - 1 = 2 and take the square root. 	ext{SE}{	ext{boot}} = \sqrt{\frac{200}{2}} = \sqrt{100} = 10. Three replicates is far too few in practice (the estimate itself is noisy), but the mechanics are the same as with ten thousand: standard deviation of the replicates. Takeaway. What…

Bootstrap standard error from three replicates

Your answer

Discussion

Learn the concepts

Related questions