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An extension of the Erdős–Neveu–Rényi theorem with applications to order statistics

✍ Scribed by M. Kaluszka; A. Okolewski

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
90 KB
Volume
55
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

The necessary and su cient conditions are given for some stochastic process to be an empirical distribution function from some exchangeable random variables. The result is applied to establish sharp lower and upper bounds for order statistics based on possibly dependent random variables.

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Consider a triangular array \(X_{1}^{n}, \ldots, X_{n}^{n}, n \in \mathbb{N}\), of rowwise independent random clements with values in a measurable space. Suppose there exists \(\theta \in[0,1)\) such that \(X_{1}^{n}, \ldots, X_{\left.\left[n^{n}\right\}\right]}^{n}\) have distribution \(v_{1}\) and