Timeline for Asymptotic Expansion of Distribution in Central Limit Theorem for Non-Identically Distributed Random Variables
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2013 at 19:55 | comment | added | Yuri Bakhtin | It looks like you are right. | |
| Sep 7, 2013 at 18:03 | comment | added | jmscarlett | After more searching, I didn't find exactly what I asked for in the question, but I did find "A Local Limit Theorem and Recurrence Conditions for Sums of Independent Non-Lattice Random Variables" (Mineka, Silverman), which turned out to be sufficient for what I need. | |
| Sep 7, 2013 at 15:47 | comment | added | jmscarlett | Thanks for the answers - Petrov's book looks quite useful, especially Section VII.1 for the lattice case. For the non-lattice case, I'm not sure that Section VI.4 is what I'm after - it looks mainly suited to random variables with a density. In particular, on p173 there is a condition $$ \sqrt{n} \int_{|t|>\varepsilon}\frac{1}{|t|}\prod_{j=1}^{n}|v_j(t)|dt \to 0 $$ for all $\varepsilon>0$, where $v_j$ is the characteristic function of the $j$-th variable in the sum. If I am not mistaken, this will generally fail for discrete non-lattice variables (please correct me if I am wrong). | |
| Sep 7, 2013 at 13:35 | history | answered | Yuri Bakhtin | CC BY-SA 3.0 |