This paper develops two weighted measures for model selection by generalizing the Kullback-Leibler divergence measure. The concept of a model selection process that takes into account the special features of the underlying model is introduced using weighted measures. New information criteria are defined using the bias correction of an expected weighted loglikelihood estimator. Using weight functions that match the features of interest in the underlying statistical models, the new information criteria are applied to simulated studies of spline regression and copula model selection. Real data applications are also given for predicting the incidence of disease and for quantile modeling of environmental data.
"Generalized predictive information criteria for the analysis of feature events." Electron. J. Statist. 7 742 - 762, 2013. https://doi.org/10.1214/13-EJS788