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PARTIALLY LINEAR MODEL SELECTION BY THE BOOTSTRAP
Author(s) -
Müller Samuel,
Vial Céline
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2009.00540.x
Subject(s) - mathematics , residual , estimator , selection (genetic algorithm) , model selection , linear model , nonparametric statistics , convergence (economics) , nonlinear system , conditional expectation , statistics , mathematical optimization , econometrics , algorithm , computer science , artificial intelligence , physics , quantum mechanics , economics , economic growth
Summary We propose a new approach to the selection of partially linear models based on the conditional expected prediction square loss function, which is estimated using the bootstrap. Because of the different speeds of convergence of the linear and the nonlinear parts, a key idea is to select each part separately. In the first step, we select the nonlinear components using an ‘ m ‐out‐of‐ n ’ residual bootstrap that ensures good properties for the nonparametric bootstrap estimator. The second step selects the linear components from the remaining explanatory variables, and the non‐zero parameters are selected based on a two‐level residual bootstrap. We show that the model selection procedure is consistent under some conditions, and our simulations suggest that it selects the true model most often than the other selection procedures considered.