Rychlik, Tomasz Bounds for expectation of \(L\)-estimates for dependent samples. (English) Zbl 0808.62048 Statistics 24, No. 1, 1-7 (1993). Summary: Accurate lower and upper bounds are presented on the expectation of each \(L\)-estimate based on a sample of possibly dependent random variables with given identical distribution functions. Distributions satisfying the bounds are constructed. Several examples are presented. Cited in 22 Documents MSC: 62G30 Order statistics; empirical distribution functions 60E15 Inequalities; stochastic orderings 62E15 Exact distribution theory in statistics Keywords:order statistic; bounds on expectation; extreme point; stochastic ordering; L-estimate; dependent random variables; identical distribution functions PDF BibTeX XML Cite \textit{T. Rychlik}, Statistics 24, No. 1, 1--7 (1993; Zbl 0808.62048) Full Text: DOI References: [1] DOI: 10.1137/0138014 · Zbl 0444.62054 · doi:10.1137/0138014 [2] DOI: 10.1016/0047-259X(85)90087-9 · Zbl 0584.62072 · doi:10.1016/0047-259X(85)90087-9 [3] Arnold B. C., Lecture Notes in Statist. 53 (1989) [4] DOI: 10.1093/biomet/61.2.387 · Zbl 0281.62012 · doi:10.1093/biomet/61.2.387 [5] DOI: 10.1214/aos/1176344567 · Zbl 0398.62036 · doi:10.1214/aos/1176344567 [6] DOI: 10.1007/BF02482542 · Zbl 0609.62070 · doi:10.1007/BF02482542 [7] DOI: 10.1080/03610928808829737 · Zbl 0639.62042 · doi:10.1080/03610928808829737 [8] DOI: 10.1080/00031305.1981.10479304 · doi:10.1080/00031305.1981.10479304 [9] Gilstein C. Z., Inst Math. Statist. Bull. 10 pp 253– (1981) [10] DOI: 10.1080/03610928208828351 · Zbl 0506.62031 · doi:10.1080/03610928208828351 [11] Hoover D. R., Statist. Prob. Letters 8 pp 261– (1989) · Zbl 0682.62033 · doi:10.1016/0167-7152(89)90131-4 [12] DOI: 10.1073/pnas.73.2.286 · Zbl 0352.60013 · doi:10.1073/pnas.73.2.286 [13] Mallows C. L., SIAM Rev. 11 pp 410– (1969) · doi:10.1137/1011075 [14] DOI: 10.1214/aoms/1177697276 · Zbl 0187.14903 · doi:10.1214/aoms/1177697276 [15] Marshall A. W., Inequalities:Theory of Majorization and its Applications (1979) [16] Rockafellar R. T., Convex Analysis (1970) · Zbl 0193.18401 · doi:10.1515/9781400873173 [17] Rychlik y, Statist. Prob. Letters 13 pp 337– (1992) · Zbl 0743.62018 · doi:10.1016/0167-7152(92)90105-E [18] DOI: 10.1080/01621459.1968.10480944 · doi:10.1080/01621459.1968.10480944 [19] DOI: 10.1007/BF02480981 · Zbl 0539.62055 · doi:10.1007/BF02480981 [20] DOI: 10.1080/00031305.1979.10482683 · doi:10.1080/00031305.1979.10482683 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.