Asymptotic optimality of a multivariate version of the generalized cross validation in adaptive smoothing splines

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We consider an adaptive smoothing spline with a piecewise-constant penalty function lambda(x), in which a univariate smoothing parameter A in the classic smoothing spline is converted into an adaptive multivariate parameter lambda. Choosing the optimal value of lambda is critical for obtaining desirable estimates. We propose to choose 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.
Publisher
INST MATHEMATICAL STATISTICS
Issue Date
2014
Language
English
Article Type
Article
Keywords

REGRESSION; GCV

Citation

ELECTRONIC JOURNAL OF STATISTICS, v.8, pp.159 - 183

ISSN
1935-7524
DOI
10.1214/14-E4S879
URI
http://hdl.handle.net/10203/193064
Appears in Collection
IE-Journal Papers(저널논문)
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