Abstract
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.
Citation
Daniel Rudolph. J. Michael Steele. "Sizes of Order Statistical Events of Stationary Processes." Ann. Probab. 8 (6) 1079 - 1084, December, 1980. https://doi.org/10.1214/aop/1176994569
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