In Philip Good's "Permutation, Parametric, and Bootstrap Tests of Hypotheses" (https://dl.acm.org/doi/10.5555/1196379), Good writes, on the topic of "Confidence Intervals Based on the Bootstrap",

The bootstrap can help us obtain an interval estimate for any aspect of a distribution... if the observations are all independent and come from distributions with the same value of the parameter to be estimated. The interval provides us with an estimate of the precision of the corresponding point estimate.

What does it mean for distributions to have a value here? Is this satisfied for estimating an arbitrary statistic $f(\text{population})$ using $f(\text{sample observations})$ provided the observations are independent?

  • 1
    $\begingroup$ The value refers to the parameter as stated. $\endgroup$
    – whuber
    Feb 6 at 15:13


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