Bootstrap examples for density estimation usually start with resampling from the empirical distribution of the "micro data", e.g. here on Normal Deviate talking about confidence intervals for nonparametric estimates of the density at some point.

But if one is interested in a property of the density (e.g. excess mass at/around a prescpecified point) is it wrong to calculate frequencies by bins, fit some flexible parametric form, and bootstrap with resampling the error, where the error is the discrepancy between the frequency in the bin vs the predicted density? This seems to be what Chetty et al. describe on page 23 (p. 25 of the PDF) of an influential paper with their posted code used in other papers since.

Does this "macro level", aggregate (block?) bootstrap do something different from resampling the empirical CDF? In any case, is the error in the parametric fit of the density the only noise we care about in the problem if we think that individual values (not frequencies) themselves have noise in them?

Larry Wasserman made a brief comment on this on his blog that

That seems unnecessary and kind of complicated. And it would add additional bias. The regular bootstrap as I described should work fine.

How bad is the additional bias? What is its source exactly?

Note the related question about whether the estimand is regular enough to bootstrap or subsample in the first place, and with what rate of convergence.

  • 1
    $\begingroup$ This is not directly relevant to the question, but note how much faster the bootstrap would be on the binned/collapsed/aggregate data than on the full micro data. $\endgroup$
    – László
    Sep 5, 2013 at 18:01


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