A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$

Berk, Kenneth N.

Ann. Probab., Tome 1 (1973) no. 5, p. 352-354 / Harvested from Project Euclid

Résumé

For each $k = 1, 2, \cdots$ let $n = n(k)$, let $m = m(k)$, and suppose $y_1^k, \cdots, y_n^k$ is an $m$-dependent sequence of random variables. We assume the random variables have $(2 + \delta)$th moments, that $m^{2 + 2/\delta}/n \rightarrow 0$, and other regularity conditions, and prove that $n^{-\frac{1}{2}}(y_1^k + \cdots + y_n^k)$ is asymptotically normal. An example showing sharpness is given.

Publié le : 1973-04-14
Classification: Central limit theorem, $m$-dependent random variables

@article{1176996992,
     author = {Berk, Kenneth N.},
     title = {A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 352-354},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996992}
}

Berk, Kenneth N. A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$. Ann. Probab., Tome 1 (1973) no. 5, pp.  352-354. http://gdmltest.u-ga.fr/item/1176996992/