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I'm moving more and more to bootstrap for my analyses to estimate the variability of parameters of glm regression models.

I usually report the bootstrap estimate of the parameter (the mean of the bootstrap distribution), but from the theory I know that the bootstrap estimate should approach the original estimate if all $n^n$ possible resamples are evaluated to build the distribution.

So I started to wonder that maybe in the results I should report the original parameter instead of the bootstrap one, together with the bootstrap derived variability statistics (eg, BCa CIs)? Or maybe the bias corrected estimate ($2*\theta-\theta^*$)?

What is the common place and the right thing to do from your experience?

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Bootstrapping is solely for estimating variability/precision not for estimating a point value. You should use the estimate based on your data and use the bootstrap standard errors or confidence interval to report precision (or p-value if you're using boostrapping for a hypothesis test).

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  • $\begingroup$ I supposed so... $\endgroup$
    – Bakaburg
    Commented Oct 14, 2015 at 20:52
  • $\begingroup$ I edited the question adding a note about the bias corrected estimate. $\endgroup$
    – Bakaburg
    Commented Oct 14, 2015 at 21:13
  • $\begingroup$ @Bakaburg if there is evidence of bias, then a bias corrected estimate would be preferred, along with some estimate of precision. $\endgroup$
    – user75138
    Commented Oct 15, 2015 at 3:46
  • $\begingroup$ Would you like to elaborate on this? $\endgroup$
    – Bakaburg
    Commented Oct 22, 2015 at 12:53

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