Model selection in regression based on pre-smoothing |
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Authors: | Marc Aerts Niel Hens Jeffrey S Simonoff |
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Institution: | 1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics , Hasselt University , Campus Diepenbeek, Agoralaan 1, B-3590 , Diepenbeek , Belgium;2. Leonard N. Stern School of Business , New York University , 44 West 4th Street, New York , NY , 10012-0258 , USA |
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Abstract: | In this paper, we investigate the effect of pre-smoothing on model selection. Christóbal et al 6 Christóbal Christóbal, J. A., Faraldo Roca, P. and González Manteiga, W. 1987. A class of linear regression parameter estimators constructed by nonparametric estimation. Ann. Statist.,, 15: 603–609. Crossref], Web of Science ®] Google Scholar] showed the beneficial effect of pre-smoothing on estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's information criterion can lead to an improved selection procedure. The bootstrap is used to control the magnitude of the random error structure in the smoothed data. The effect of pre-smoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model. |
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Keywords: | Akaike information criterion fractional polynomial latent variable model model selection pre-smoothing |
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