Truong, Young K. Asymptotic properties of kernel estimators based on local medians. (English) Zbl 0675.62031 Ann. Stat. 17, No. 2, 606-617 (1989). Summary: The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence \(n^{-1/(2+d)}\) both pointwise and in the \(L^ q\) \((1\leq q<\infty)\) norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence \((n^{- 1}\log n)^{1/(2+d)}\) in the \(L^{\infty}\) norm restricted to a compact. These results also constitute an answer to an open question of C. J. Stone [ibid. 10, 1040-1053 (1982; Zbl 0511.62048)]. Cited in 31 Documents MSC: 62G05 Nonparametric estimation 62E20 Asymptotic distribution theory in statistics Keywords:nonparametric regression; conditional median function estimation; sequence of local median estimators; optimal rate of convergence Citations:Zbl 0511.62048 PDFBibTeX XMLCite \textit{Y. K. Truong}, Ann. Stat. 17, No. 2, 606--617 (1989; Zbl 0675.62031) Full Text: DOI