Central Limit Theorems for Sums of Dependent Vector Variables

Cocke, W. J.

Cocke, W. J.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 968-976 / Harvested from Project Euclid

Résumé

We prove the following central limit theorems for sums of mutually dependent random vector variables: Given that a sequence of random vector variables satisfies a certain type of decoupling condition (and two milder restrictions), we present a Lindeberg-Feller condition which we show to be both necessary and sufficient for central limit behavior. The decoupling condition and one of the two milder conditions is then applied to a Markov process with stationary transition mechanism.

Publié le : 1972-06-14
Classification:

@article{1177692559,
     author = {Cocke, W. J.},
     title = {Central Limit Theorems for Sums of Dependent Vector Variables},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 968-976},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692559}
}

Cocke, W. J. Central Limit Theorems for Sums of Dependent Vector Variables. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  968-976. http://gdmltest.u-ga.fr/item/1177692559/