Bootstrapping skewed data

1. Can a bootstrap distribution be skewed?
2. Does bootstrapping assume normal distribution?
3. Is bootstrapping unbiased?
4. What is the problem with bootstrapping?

Can a bootstrap distribution be skewed?

The bootstrap distribution is positively skewed (skewed to the right), correctly suggesting that the sampling distribution of the mean is asymmetric. This is correct because we draw the data from a lognormal distribution and not from a normal distribution, as assumed by the T- distribution in Figure 1B.

Does bootstrapping assume normal distribution?

Bootstrapping does not make assumptions about the distribution of your data. You merely resample your data and use whatever sampling distribution emerges. Then, you work with that distribution, whatever it might be, as we did in the example.

Is bootstrapping unbiased?

Like jackknife statistics, bootstrap estimators are not assumed to be unbiased estimators of the population parameter. Instead it is assumed that, if the sample statistic ( ) provides a biased estimate of its parameter ( Θ ), the bootstrap statistic ( ^* ) provides a similarly biased estimate of the sample statistic.

What is the problem with bootstrapping?

It does not perform bias corrections, etc. There is no cure for small sample sizes. Bootstrap is powerful, but it's not magic — it can only work with the information available in the original sample. If the samples are not representative of the whole population, then bootstrap will not be very accurate.