Given a process $\{X_i\}$, any permutation $\sigma: \lbrack 1, n\rbrack \rightarrow \lbrack 1, n\rbrack$ determines an order statistical event $A(\sigma) = \{X_{\sigma(1)} < X_{\sigma(2)} < \cdots < X_{\sigma(n)}\}$. How many events $A(\sigma)$ are needed to form a union whose probability exceeds $1 - \epsilon$? This question is answered in the case of stationary ergodic processes with finite entropy.
Publié le : 1980-12-14
Classification:
Order statistics,
entropy,
stationary processes,
de Bruijn sequences,
directed graphs,
equipartition property,
60G10,
60005
@article{1176994569,
author = {Rudolph, Daniel and Steele, J. Michael},
title = {Sizes of Order Statistical Events of Stationary Processes},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 1079-1084},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994569}
}
Rudolph, Daniel; Steele, J. Michael. Sizes of Order Statistical Events of Stationary Processes. Ann. Probab., Tome 8 (1980) no. 6, pp. 1079-1084. http://gdmltest.u-ga.fr/item/1176994569/