Hušková, Marie; Jurečková, Jana Asymptotic representation of R-estimators of location. (English) Zbl 0594.62042 Probability and statistical decision theory, Proc. 4th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf/Austria 1983, Vol. A, 145-165 (1985). Summary: [For the entire collection see Zbl 0579.00015.] Bahadur-type representations of Hodges-Lehmann’s type rank estimators of location are derived. Depending on the continuity and/or discontinuity of the score function of the pertaining rank test and on its behavior in the neighborhood of 0 and 1, the orders of the representations are \(O_ p(n^{-1/4})\), \(O_ p(n^{-1/2}\log n)\) and \(O_ p(n^{-1/2})\), respectively. Cited in 1 Document MSC: 62G05 Nonparametric estimation Keywords:asymptotic representation; R-estimators; signed-rank statistics; second order asymptotic linearity; Bahadur-type representations; Hodges- Lehmann’s type rank estimators of location; score function Citations:Zbl 0579.00015 PDFBibTeX XML