Summary
Based on an (almost sure) reverse-martingale representation for linear combinations of order statistics (with smooth weight functions), a backward invariance principle (relating to the tail sequence) is established and the underlying regularity conditions are critically examined.
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Work supported by the Air Force Office of Scientific Research, AFSC, USAF, Contract No. AFOSR 74-2736. Reproduction in whole or part is permitted for any purpose of the U.S. Government
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Kumar Sen, P. An invariance principle for linear combinations of order statistics. Z. Wahrscheinlichkeitstheorie verw Gebiete 42, 327–340 (1978). https://doi.org/10.1007/BF00533468
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DOI: https://doi.org/10.1007/BF00533468