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Sizes of Order Statistical Events of Stationary Processes

Daniel Rudolph and J. Michael Steele
The Annals of Probability
Vol. 8, No. 6 (Dec., 1980), pp. 1079-1084
Stable URL: http://www.jstor.org/stable/2243009
Page Count: 6
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Sizes of Order Statistical Events of Stationary Processes
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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.

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