【摘 要】
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For semiparametric regression model selection, based on a model selection criterion there is no finite order (or number of parameters) of the nonparametric part
【机 构】
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Departm ent of Probability and Statistics, Peking University, Beijing 100871, China
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For semiparametric regression model selection, based on a model selection criterion there is no finite order (or number of parameters) of the nonparametric part to be estimated consistently, but there is a finite order (or number of predictor variables) of the linearpart to be estimated consistently. The models selected by using AIC and AICC are not consistent estimates of linear part of the true model. In this paper, we study the consistency in model selection by investigating the asymptotic properties of AIC* and AICC*, the modified versions of AIC and AICC respectively, which were proposed by a referee of the reference Shi and Tsai. Under some regular conditions, we prove that the parametric models of the semiparametric regression selected with AIC* and AICC*converge to the true model in probability. In addition, in terms of the mean integrated squared errcr plus a penalty, these two criteria can also provide an asymptotically efficient selection.
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