Bootstrap confidence intervals on parameters or on distribution?

Excuse what may be an obvious question about bootstrapping. I got sucked in the Bayesian world early and never really explored bootstrapping as much as I should have.

I ran across an analysis in which the authors were interested in a survival analysis related to some time to failure data. They had about 100 points and used regression to fit a Weibull distribution to the data. A result of this they obtained estimates of the scale and shape parameters. A very traditional approach. However, they next used bootstrapping to sample from the original data set and, for each new sample, performed a regression and came up with a new Weibull distribution. The results of the bootstrapping was then used to construct confidence intervals on the survival distribution.

My intuition is a bit conflicted. I’m familiar with bootstrapping confidence intervals on parameters, but not seen it used for constructing distribution confidence intervals.

Can anyone point me toward a reference/source that might provide some insight? Thanks in advance.

Answer

Basically, if you have a joint confidence interval for the parameters that uniquely describe a distribution, then you have a distribution confidence interval. So your problem vanishes… as per whuber’s comment.

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Source : Link , Question Author : Aengus , Answer Author : Peter Ellis

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