Vainer, B. P.; Kukush, O. G. The consistency of \(M\)-estimates constructed from a concave weight function. (English. Ukrainian original) Zbl 0933.62057 Theory Probab. Math. Stat. 57, 11-18 (1998); translation from Teor. Jmovirn. Mat. Stat. 57, 10-17 (1997). A model of nonlinear regression in the structured case is considered. The \(M\)-estimator of the regression parameter, which has robustness properties by convex scaled functions, is constructed and its strong consistency is proved. Contrast inequalities for unimodal distributions of rates of observations are found. Also, the case of Gaussian rates in an infinite-dimensional Hilbert space is studied. Reviewer: A.V.Swishchuk (Kyïv) Cited in 1 Document MSC: 62J02 General nonlinear regression 62G35 Nonparametric robustness 62G05 Nonparametric estimation 62H12 Estimation in multivariate analysis 62G20 Asymptotic properties of nonparametric inference Keywords:M-estimators; consistency; convex scaled functions PDFBibTeX XMLCite \textit{B. P. Vainer} and \textit{O. G. Kukush}, Teor. Ĭmovirn. Mat. Stat. 57, 10--17 (1997; Zbl 0933.62057); translation from Teor. Jmovirn. Mat. Stat. 57, 10--17 (1997)