Abstract
Asymptotic properties of the generalized information criterion for model selection are examined and new conditions under which this criterion is overfitting, consistent, or underfitting are derived.
Highlights
Generalized information criterionConsider a family of probability distributions, f (z; θ), where z ∈ Rd+1 consisting of both response, y, and explanatory variables, x ∈ Rd, and θ ∈ Θ ⊂ Rm is a set of parameters
Where α ≥ 0 is the tuning parameter, and κ(Sk) is the model size defined as the number of elements in Sk
Assume the true model consists of the variable x3
Summary
Consider a family of probability distributions, f (z; θ), where z ∈ Rd+1 consisting of both response, y, and explanatory variables, x ∈ Rd, and θ ∈ Θ ⊂ Rm is a set of parameters. Where α ≥ 0 is the tuning parameter, and κ(Sk) is the model size defined as the number of elements in Sk. Let Skn ∈ S be the model selected by gic. We use the terms overfitting and underfitting as defined in the sense of efficiency by [4]. In this framework, model selection is to find the best model that is either a true model or a model closest to the true model. The overfitting implies the model has a larger likelihood value
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