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Just a note

If the mean bias of your estimator is E[] - Θ then you can estimate it, from B bootstrap estimates, as Σ*/B - .

So, where < Σ*/B, you would assume your estimator was biased positively, and on average that Θ < < Σ*/B.

For a biased estimator, you could estimate its variance as the summed squared deviations of your bootstrap estimators from their mean. ( Σ[* - Σ*/B]2 / B )

If however * is obviously asymmetric, and this cannot be corrected by transformation, a median bias may be more appropriate. Of course, if the estimator is known to be unbiased, the observed estimate ( ) can replace of Σ*/B - which simplifies the variance estimate to Σ[* - ]2 / B.