Abstract
Selection from finite sets is a basic procedure of statistics and the partial sum behavior of selected elements is completely known under the “uniform asymptotic negligibility” condition of central limit theory. The purpose of the present paper is to determine the asymptotic behavior of partial sums when the central limit theorem fails. As an application, we describe the limiting properties of permutation and bootstrap statistics in case of infinite variance.
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Dedicated to the memory of Sándor Csörgő.
I. Berkes’s research was supported by OTKA grants K 61052, K 67961, FWF grant S 9603-N23, and NSF-OTKA grant INT-0223262. L. Horváth’s research was supported by NSF grant DMS 0604670.
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Berkes, I., Horváth, L. & Schauer, J. Non-central limit theorems for random selections. Probab. Theory Relat. Fields 147, 449–479 (2010). https://doi.org/10.1007/s00440-009-0212-z
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DOI: https://doi.org/10.1007/s00440-009-0212-z
Keywords
- Random selection
- Uniform asymptotic negligibility
- Bootstrap
- Functional limit theorems
- Permutation statistics
Mathematics Subject Classification (2000)
- Primary 60F17
- 62F40