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

1984; Institute of Mathematical Statistics; Volume: 12; Issue: 1 Linguagem: Inglês

10.1214/aos/1176346393

2168-8966

Robert Serfling,

Statistical Distribution Estimation and Applications

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.