Central Limit Theorems and the Deeper Naivete

When you are young, you learn the iid Central Limit Theorem. They call it “Classical” which we all know is math-code for “Lame”.

Then, as you advance through your training, you study Lindeberg conditions and mixing coefficients. You study and learn the requirements for triangular arrays and martingales.

Finally, when at last you are old, you embrace the Deeper Naivete: any sum of random variables is probably sort of normally distributed in the end, and it’s definitely not worth checking.

Zach

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