As central limit theorem suggests, sampling distribution is approaching normal on the large sample sizes regardless of the initial distribution of the variable.
And it's always been true for me until I stumbled on this one.
I have a sample of 50K observation. I want to bootstrap a confidence interval around the mean. I take a sample of size 20K with replacement, calculate its mean and repeat it 10,000 times. Then I plot a histogram of it and what I expect to see is something like normal distribution (as always). However, what I see is this:
Now the questions: how come that initial sampling distribution did not have approximately normal shape (1) and, as logic suggests, does that mean that bootstrapping is fragile to outliers even with such a large sample sizes and number of repetitions 10,000 and even 100,000 times (2)?