Adaptive nonparametric estimation of a multivariate regression function
type: Item
instance of: scholarly article
title: Adaptive nonparametric estimation of a multivariate regression function
zbMATH Open document ID: 0653.62030
DOI: 10.1016/0047-259X(87)90151-5
author: Y. P. Mack
author: Hans-Georg Müller
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4066147
zbMATH Keywords: bias
zbMATH Keywords: variance
zbMATH Keywords: asymptotic normality
zbMATH Keywords: tightness
zbMATH Keywords: kernel estimation
zbMATH Keywords: multivariate regression function
zbMATH Keywords: bandwidth
zbMATH Keywords: minimum mean squared error
zbMATH Keywords: adaptive estimates
zbMATH Keywords: efficient data-driven consistent estimation
zbMATH Keywords: data- driven local scaling
zbMATH Keywords: nearest-neighbor-type estimates
zbMATH Keywords: variance- stabilizing estimates
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4066147