I'll give an introductory review on a method for model selection known as Generalized cross-validation (GCV) (see linked paper). When dealing with linear predictor models, GCV provides a computationally convenient approximation to "leave-one-out" cross-validation. I'll discuss this connection between cross-validation and GCV in more detail. I'll then discuss attempts in the literature made at extending the idea behind GCV to more general models in the exponential family.
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