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September, 1985 Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$
Michael Nussbaum
Ann. Statist. 13(3): 984-997 (September, 1985). DOI: 10.1214/aos/1176349651

Abstract

For nonparametric regression estimation on a bounded interval, optimal rates of decrease for integrated mean square error are known but not the best possible constants. A sharp result on such a constant, i.e., an analog of Fisher's bound for asymptotic variances is obtained for minimax risk over a Sobolev smoothness class. Normality of errors is assumed. The method is based on applying a recent result on minimax filtering in Hilbert space. A variant of spline smoothing is developed to deal with noncircular models.

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Michael Nussbaum. "Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$." Ann. Statist. 13 (3) 984 - 997, September, 1985. https://doi.org/10.1214/aos/1176349651

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0596.62052
MathSciNet: MR803753
Digital Object Identifier: 10.1214/aos/1176349651

Subjects:
Primary: 62G20
Secondary: 41A15, 62G05, 65D10

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September, 1985
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