Asymptotic properties of linear functions of order statistics (Q1107232)
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scientific article; zbMATH DE number 4064245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic properties of linear functions of order statistics |
scientific article; zbMATH DE number 4064245 |
Statements
Asymptotic properties of linear functions of order statistics (English)
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1988
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Let \(X_{r:n}\) be the r-th order statistic of a sample of size n. Let \(T_ n\) be the arithmetical mean of \(J(r/(n+1))h(X_{r:n})\), where both J(.) and h(.) are some smooth functions (specified in the paper). The authors establish an almost sure approximation to \(T_ n\), from which asymptotic normality and an iterated logarithm theorem are deduced.
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linear functions of order statistics
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almost sure representation
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Wiener process embedding
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invariance principle
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arithmetical mean
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smooth functions
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almost sure approximation
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asymptotic normality
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iterated logarithm theorem
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