Semiparametric Bayesian Information Criterion for Model Selection in Ultra-high Dimensional Additive Models

2011/07/25 by Heng Lian, Lian, Heng
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1107.4861

openalex publication_date 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little justification that the effects of the covariates are actually linear. Thus a semiparametric model such as the additive model studied here, is a viable alternative. We demonstrate that theoretical results on the consistency of BIC-type criterion can be extended to this more challenging situation, with dimension diverging exponentially fast with sample size. Besides, the noise assumptions are relaxed in our theoretical studies. These efforts significantly enlarge the applicability of the criterion to a more general class of models.

Citations

• Nearly unbiased variable selection under minimax concave penalty

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