Summary
A general class of statistics based on sequential ranks is introduced. Under suitable regularity conditions, an almost sure representation and invariance principle are established for this class. In particular, it is shown that these statistics can obey invariance principles that are radically different from those obeyed by the usual full rank statistics.
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Research supported by the CSIR and the University of South Africa
Research supported by the University of Delaware Research Foundation, Grant #8325530015
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Lombard, F., Mason, D.M. Limit theorems for generalized sequential rank statistics. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 395–410 (1985). https://doi.org/10.1007/BF00534871
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DOI: https://doi.org/10.1007/BF00534871