<p>Theorem 2.1 in <a href="https://arxiv.org/ftp/arxiv/papers/1809/1809.04016.pdf" rel="noreferrer">Horowitz (2019)</a> is what you are looking for</p>

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2021-07-06T16:52:33.773Z
2021-07-06T16:52:33.773Z
Kyle Butts
<p>If an estimator is known to have an asymptotically normal distribution, is that sufficient for the bootstrap to be valid?</p>
<p>It seems that is must be, but in 20 minutes of Googling I have come up empty on a proof.</p>

<econometrics><causal-inference>
Bootstrap always valid under asymptotic Normality?
Michael Gmeiner
# Bootstrap always valid under asymptotic Normality?

(Asked by: username_0 on 2021-07-06)

If an estimator is known to have an asymptotically normal distribution, is that sufficient for the bootstrap to be valid?

It seems that is must be, but in 20 minutes of Googling I have come up empty on a proof.

**Tags:** econometrics, causal-inference


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## 1 answers

### Answer by username_1 on 2021-07-06. Score: 5 | Accepted answer

Theorem 2.1 in [Horowitz (2019)](https://arxiv.org/ftp/arxiv/papers/1809/1809.04016.pdf) is what you are looking for


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