Error in Central Limit Theorem for i.i.d. random variables with atomic distribution

Error in Central Limit Theorem for i.i.d. random variables with atomic distribution

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Dmitry Dolgopyat , University of Maryland
Jadwin Hall 111

We consider sums of independent identically distributed random variables whose distributions have d atoms. Such distributions never admit an Edgeworth expansion of order d-1 but we show that for almost all parameters the Edgeworth expansion of order d-2 is valid and the error of the order d-1 Edgeworth expansion is typically of order n^{-(d-1)/2}. This is a joint work with Kasum Fernando.