Generalized $L-, M-$, and $R$-Statistics

Other literature type English OPEN
Serfling, Robert J. (1984)
  • Publisher: The Institute of Mathematical Statistics
  • Journal: (issn: 0090-5364)
  • Related identifiers: doi: 10.1214/aos/1176346393
  • Subject: Order statistics | $L$-statistics | $M$-statistics | $R$-statistics | Hodges-Lehmann estimator | trimmed $U$-statistics | asymptotic normality | 62E20 | 60F05

A class of statistics generalizing $U$-statistics and $L$-statistics, and containing other varieties of statistic as well, such as trimmed $U$-statistics, is studied. Using the differentiable statistical function approach, differential approximations are obtained and the influence curves of these generalized $L$-statistics are derived. These results are employed to establish asymptotic normality for such statistics. Parallel generalizations of $M$- and $R$-statistics are noted. Strong convergence, Berry-Esseen rates, and computational aspects are discussed.
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