# Are predictions generated from bootstrap resampling normally distributed?

If I resample a dataset hundreds of times with replacement (bootstrap replications), fit some Model A on each bootstrap sample, and generate predictions (time series) from each fitted model, can I expect the aggregate of the predictions (bagging) to collectively have a normal distribution?

I ask because there are many instances in statistics where if the number of observations goes up, the more random samples will collectively appear normally distributed.

• So you're talking about multiple bootstraps? Boot strap, aggregate, repeat? Jul 8 '20 at 23:01
• yeah, bootstrap $T$-length time series $B=200$ times, then aggregate each of those $200$ replications (time series) into $200$ average prediction or performance measure. Would we expect the $200$ aggregated predictions to be normally distributed just because the resamplings fed into the data were also drawn from the same full sample distribution? or are there specific conditions for the aggregate output to appear normal? Jul 8 '20 at 23:23
• Generally, no. Imagine a model bounded below by 0 (logistic regression is an example). Floor effects would prevent this from looking symmetric. Jul 8 '20 at 23:38
• sorry i dont follow ur answer. I think there would be a mass of observations at some central tendency, and a few outliers forming the tails Jul 9 '20 at 0:54
• Increasing T would often make things look more normal. Increasing B should only get you nearer to the bootstrap sampling distribution (a clearer picture of an unchanging target) Jul 9 '20 at 1:47
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