I am hoping somebody can explain/confirm for me the intuition behind the bias-adjusted confidence intervals that are provided by bootstrap, and explained on page 20 and 21 here: https://www.stata.com/manuals13/rbootstrap.pdf.
My understanding is that the percentile CIs given by e(ci_percentile) provide, under the default confidence level(95), the 5th and 95th percentile of the bootstrapped distribution of my calculated parameter-- i.e., the distribution of the bootstrapped parameter values. These confidence intervals make sense for a parameter with a non-normal distribution, if I'm right.
I am not sure of my intuition of the bias-adjusted confidence intervals e(ci bc). I think I understand the (page 20) parameter zo --- if the parameter value 0.5 holds 1/3 of my bootstrapped distribution, then zo for theta = 0.5 is the value which would hold 1/3 of the data under a standard normal distribution. But I don't understand the intuition behind the (page 20) parameter a, and so I don't really follow equations defining p1 and p2 defined at the bottom of page 20. My best guess is that p1 and p2 are providing the confidence intervals for a normally distributed parameter, but adjusting/correcting for slight differences between the standard normal and the bootstrapped, close-to-normal distribution? If this is true, great, but I'd love to actually understand the parameter a, and the precise correction being performed. For instance, I have no idea what it means that the non-accelerated version assumes a=0, which means that I'mm not sure when one would use e(ci bc)vs e(ci bca).
Thank you!
My understanding is that the percentile CIs given by e(ci_percentile) provide, under the default confidence level(95), the 5th and 95th percentile of the bootstrapped distribution of my calculated parameter-- i.e., the distribution of the bootstrapped parameter values. These confidence intervals make sense for a parameter with a non-normal distribution, if I'm right.
I am not sure of my intuition of the bias-adjusted confidence intervals e(ci bc). I think I understand the (page 20) parameter zo --- if the parameter value 0.5 holds 1/3 of my bootstrapped distribution, then zo for theta = 0.5 is the value which would hold 1/3 of the data under a standard normal distribution. But I don't understand the intuition behind the (page 20) parameter a, and so I don't really follow equations defining p1 and p2 defined at the bottom of page 20. My best guess is that p1 and p2 are providing the confidence intervals for a normally distributed parameter, but adjusting/correcting for slight differences between the standard normal and the bootstrapped, close-to-normal distribution? If this is true, great, but I'd love to actually understand the parameter a, and the precise correction being performed. For instance, I have no idea what it means that the non-accelerated version assumes a=0, which means that I'mm not sure when one would use e(ci bc)vs e(ci bca).
Thank you!
