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In this work, the method of random forests (RF) was applied for modeling and prediction of the relative retention time of some polybrominated diphenylethers (PBDEs) with descriptors calculated from the molecular structure alone. The effects of tuning parameters such as the number of trees (n t ) and the number of randomly selected variables to split each node (m) were investigated. The obtained results showed that the pair (m ¼ 38, n t ¼ 500) can be considered as a plausible setting so that the generalization error was minimal. Also, the importance level of different descriptors was evaluated using RF to simplify the model. The performance of the RF model was compared with the artificial neural network (ANN). Both ANN and RF methods provided accurate predictions, although more accurate results were obtained by the RF model. The determination coefficients of the test set, obtained by the ANN and RF methods, are 0.9619 and 0.9707 respectively.

In this paper, we introduce a two-step procedure, in the context of ultrahigh-dimensional additive models, to identify nonzero and linear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments to evaluate the numerical performance of the proposed method and analyze a cardiomyopathy microarray data for an illustration. Numerical studies confirm the fine performance of the proposed method for various semiparametric models.