The Annals of Statistics

Approximation of Method of Regularization Estimators

Dennis D. Cox

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Abstract

The Tikhonov method of regularization (MOR) estimator provides a general method for estimation of a nonparametric regression parameter in an abstract linear model with discrete noisy data. An asymptotic analysis is given in which the discrete estimation problem is approximated by a continuous one. Rates of convergence are calculated in a family of norms natural to the problem. The general theory is applied to the estimation of functions from noisy evaluations of the function and one of its derivatives.

Article information

Source
Ann. Statist., Volume 16, Number 2 (1988), 694-712.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350829

Digital Object Identifier
doi:10.1214/aos/1176350829

Mathematical Reviews number (MathSciNet)
MR947571

Zentralblatt MATH identifier
0671.62044

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 41A25: Rate of convergence, degree of approximation 47A50: Equations and inequalities involving linear operators, with vector unknowns

Keywords
41-00 Nonparametric regression method of regularization smoothing splines rates of convergence

Citation

Cox, Dennis D. Approximation of Method of Regularization Estimators. Ann. Statist. 16 (1988), no. 2, 694--712. doi:10.1214/aos/1176350829. https://projecteuclid.org/euclid.aos/1176350829


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