Härdle, W.; Janssen, P.; Serfling, R. Strong uniform consistency rates for estimators of conditional functionals. (English) Zbl 0672.62050 Ann. Stat. 16, No. 4, 1428-1449 (1988). Let (X,Y) be a bivariate random vector with joint distribution function (df) F(x,y) and conditional df F(y\(| x)\). Let \(\{\beta_ t\), \(t\in I\}\) be a family of real-valued measurable functions on R for which it is desired to estimate \[ r_ t(X)=E\{\beta_ t(Y)| X=x\}=\int \beta_ t(y)dF(y| x) \] such that a good almost sure convergence rate holds uniformly for \(\in I,\) where I is a possibly infinite (or degenerate) interval in R. The present treatment unifies a number of specific problems previously studied separately in the literature. The authors treat some of these applications in detail, including regression curve estimation, density estimation, estimation of conditional df’s, L- smoothing and M-smoothing. Reviewer: M.A.Mirzahmedov Cited in 3 ReviewsCited in 54 Documents MSC: 62G05 Nonparametric estimation 60F15 Strong limit theorems Keywords:almost sure convergence rate; regression curve estimation; density estimation; L-smoothing; M-smoothing PDFBibTeX XMLCite \textit{W. Härdle} et al., Ann. Stat. 16, No. 4, 1428--1449 (1988; Zbl 0672.62050) Full Text: DOI