B0777
Title: Some optimality properties of FDR controlling modifications of AIC and BIC in high dimensions
Authors: Florian Frommlet - Medical University Vienna (Austria) [presenting]
Malgorzata Bogdan - Lund University (Sweden)
Abstract: Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood in case of a moderate number of variables. However, these criteria do not work well in a high-dimensional setting under the assumption of sparsity. We will introduce different modifications of AIC and BIC which will allow to control the family wise error rate (mAIC, mBIC) or the false discovery rate (mAIC2, mBIC2), respectively, in terms of including false positive regressors in the model. Our modifications of BIC have a nominal level which is roughly indirect proportional to the square root of the sample size, whereas the modifications of AIC have a fixed nominal level. We will discuss for which purpose one might prefer mAIC2 or mBIC2 and give the conditions under which they provide selection procedures which are asymptotically Bayes optimal under sparsity (ABOS). Finally we want to compare their performance in the context of GWAS data.
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