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 Krieger and Pickands (Ann. Statist.9 (1981) 1066-1078) and Abramson (J. Multivariate Anal.12 (1982), 562-567) 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.
Year of publication: |
1987
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Authors: | Mack, Y.P. ; Mu¨ller, Hans-Georg |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 23.1987, 2, p. 169-183
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Publisher: |
Elsevier |
Subject: | multivariate kernel regression estimation bias variance asymptotic normality mean square error tightness weak convergence in C[a | b] Gaussian process adaptation |
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