Basic bootstrap interval for a skewed correlation

Question

Your estimated correlation on the original sample is $\hat{\theta} = 0.30$ . The bootstrap distribution is skewed: its 2.5th percentile is $0.10$ and its 97.5th percentile is $0.55$ .

Construct the 95% basic (reverse-percentile) bootstrap confidence interval.

Accepted Answer

The basic interval reflects the bootstrap quantiles through twice the estimate, swapping the tails: \left[\, 2\hat{	heta} - q{0.975}, \;\; 2\hat{	heta} - q{0.025} \,ight]. Plug in \hat{	heta} = 0.30, q{0.025} = 0.10, q{0.975} = 0.55. 	ext{lower} = 2(0.30) - 0.55 = 0.60 - 0.55 = 0.05, 	ext{upper} = 2(0.30) - 0.10 = 0.60 - 0.10 = 0.50. So the basic interval is [0.05, 0.50]. The bootstrap distribution leaned right (its upper tail, 0.55 - 0.30 = 0.25, is longer than its lower tail, 0.30 - 0.10 = 0.20). The basic interval flips that: it stretches further below \hat{	heta} than above, becau…

Basic bootstrap interval for a skewed correlation

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