I have a question about the Central Limit Theorem in the context of estimating a population parameter through a sample statistic.
The most known case is that the CLT asserts that a sampling distribution of the means will become approximately a normal distribution for a large sample size. I saw this also works for the sampling distribution of the proportion.
As I understood the CLT doesn't generally guarantee the sampling distibution to be normal for arbitrary sample statistics. Are there any other sample statistics for which the CLT does so, and if so, for which?