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2014 Asymptotic optimality of a multivariate version of the generalized cross validation in adaptive smoothing splines
Heeyoung Kim, Xiaoming Huo
Electron. J. Statist. 8(1): 159-183 (2014). DOI: 10.1214/14-EJS879

Abstract

We consider an adaptive smoothing spline with a piecewise-constant penalty function $\lambda(x)$, in which a univariate smoothing parameter $\lambda$ in the classic smoothing spline is converted into an adaptive multivariate parameter $\boldsymbol{\lambda}$. Choosing the optimal value of $\boldsymbol{\lambda}$ is critical for obtaining desirable estimates. We propose to choose $\boldsymbol{\lambda}$ by minimizing a multivariate version of the generalized cross validation function; the resulting estimator is shown to be consistent and asymptotically optimal under some general conditions—i.e., the counterparts of the nice asymptotic properties of the generalized cross validation in the ordinary smoothing spline are still provable. This provides theoretical justification of adopting the multivariate version of the generalized cross validation principle in adaptive smoothing splines.

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Heeyoung Kim. Xiaoming Huo. "Asymptotic optimality of a multivariate version of the generalized cross validation in adaptive smoothing splines." Electron. J. Statist. 8 (1) 159 - 183, 2014. https://doi.org/10.1214/14-EJS879

Information

Published: 2014
First available in Project Euclid: 12 February 2014

zbMATH: 1282.62101
MathSciNet: MR3165437
Digital Object Identifier: 10.1214/14-EJS879

Subjects:
Primary: 62G20
Secondary: 62G08

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 1 • 2014
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