By I Ekeland

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Comput. Stat. Data Anal. 56(5), 1038–1051 (2012) 9. : On the choice of a model to fit data from an exponential family. Ann. Stat. 16(1), 342–355 (1988) 10. : Adaptive estimation of a quadratic functional by model selection. Ann. Stat. 28(5), 1302–1338 (2000) 11. : Selection consistency of EBIC for GLIM with non-canonical links and diverging number of parameters. Stat. Interface 6(2), 275–284 (2013) 12. : Extended Bayesian information criterion in the Cox model with a high-dimensional feature space.

Ii-c) Combining the bounds. n/ 125c 20F jJj change 1A A @1 ˙ @eF1 aMLE CF2 C 2 C C clower n c3lower (16) for sufficiently large n, as desired. Remark 2 The proof of Theorem 1 could be modified to handle other situations of interest. n/=n. J/aMLE that would appear in (16) could be compensated using (14) in less crude of a way than when moving to (15). 4 Numerical Experiment for Sparse Bayesian Logistic Regression In this section, we perform a simulation study to assess the approximation error in Laplace approximations to the marginal likelihood of logistic regression models.

2 I k here K is the number of folds, fk is the set of indices of the samples in fold k, and yO i k . / is the fitted predicted value for observation i when fold k involving observation i, is left out of the estimation. Preselection for Genomic Exploration 41 We illustrate the property of freezing in an example based on a random simulation run from the experiments described in Sect. 3. The top black curve in Fig. 1a is the cross-validation curve for the full data set with all covariates. The global minimum of this curve is located in and we call the selected variables using , the global solution.

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