Model Selection for Nonparametric Regression Yang, Yuhong
dc.contributor.department Statistics 2018-02-16T21:35:13.000 2020-07-02T06:55:48Z 2020-07-02T06:55:48Z 1997
dc.description.abstract <p>Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle selection bias. Resulting estimators are shown to achieve a trade-off among approximation error, estimation error and model complexity without prior knowledge about the true regression function. We demonstrate the adaptability of these estimators over full and sparse approximation function classes with different smoothness. For high-dimensional function estimation by tensor product splines we show that with number of knots and spline order adaptively selected, the least squares estimator converges at anticipated rates simultaneously for Sobolev classes with different interaction orders and smoothness parameters.</p>
dc.description.comments <p>This preprint was published as Yuhong Yang, "Model Selection for Nonparametric Regression", <em>Statistics Sinica</em> (1999): 475-499.</p>
dc.identifier archive/
dc.identifier.articleid 1104
dc.identifier.contextkey 7444389
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath stat_las_preprints/101
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:13:38 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords adaptive estimation
dc.subject.keywords model complexity
dc.subject.keywords model selection
dc.subject.keywords nonparametric regression
dc.subject.keywords rates of convergence
dc.title Model Selection for Nonparametric Regression
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
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