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October, 1971 A Weak Convergence Theorem for Order Statistics From Strong-Mixing Processes
Roy E. Welsch
Ann. Math. Statist. 42(5): 1637-1646 (October, 1971). DOI: 10.1214/aoms/1177693162


This paper provides sufficient conditions for the weak convergence in the Skorohod space $D^d\lbrack a, b\rbrack$ of the processes $\{(Y_{1,\lbrack nt\rbrack} - b_n)/a_n, (Y_{2,\lbrack nt\rbrack} - b_n)/a_n, \cdots, (Y_{d,\lbrack_{nt\rbrack}} - b_n)/a_n\}, 0 < a \leqq t \leqq b$, where $Y_{i,n}$ is the $i$th largest among $\{X_1, X_2, \cdots, X_n\}, a_n$ and $b_n$ are normalizing constants, and $\langle X_n: n \geqq 1\rangle$ is a stationary strong-mixing sequence of random variables. Under the conditions given, the weak limits of these processes coincide with those obtained when $\langle X_n: n \geqq 1\rangle$ is a sequence of independent identically distributed random variables.


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Roy E. Welsch. "A Weak Convergence Theorem for Order Statistics From Strong-Mixing Processes." Ann. Math. Statist. 42 (5) 1637 - 1646, October, 1971.


Published: October, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0244.60008
MathSciNet: MR383507
Digital Object Identifier: 10.1214/aoms/1177693162

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 5 • October, 1971
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