Adaptive nonparametric estimation of a multivariate regression function
We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of \textit{A. M. Krieger} and \textit{J. Pickands} [Ann. Stat. 9, 1066-1078 (1981; Zbl 0478.62027)] and \textit{I. S. Abramson} [J. Multivariate Anal. 12, 562-567 (1982; Zbl 0515.62032)] in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.
efficient data-driven consistent estimation
scientific article; zbMATH DE number 4066147
scientific article