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A weight-relaxed model averaging approach for high-dimensional generalized linear models. (English) Zbl 1421.62094
T. Ando and K.-C. Li [J. Am. Stat. Assoc. 109, No. 505, 254–265 (2014; Zbl 1367.62209)] proposed a method of model averaging that allows the number of predictors to increase as the sample size increases. In the paper under review, the results are extended from linear to a generalized linear regression model based on the one-parameter exponential family. The existence and uniqueness of pseudotrue regression parameters is shown under model misspecification. Proper conditions are derived for the leave-one-out cross-validation weight selection to achieve asymptotic optimality. Simulations illustrate the merits of the proposed procedure over several methods, including the Lasso, the Akaike and Bayesian information criterion model-averaging methods and some other regularization methods.

MSC:
62J12 Generalized linear models (logistic models)
62F99 Parametric inference
62F12 Asymptotic properties of parametric estimators
62B10 Statistical aspects of information-theoretic topics
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