In several instances of statistical
practice, it is not uncommon to use the same data for both model selection and
inference, without taking account of the variability induced by model selection
step. This is usually referred to as post-model selection inference. The
shortcomings of such practice are widely recognized, finding a general solution
is extremely challenging. We propose a model averaging alternative consisting
on taking into account model selection probability and the like-lihood in
assigning the weights. The approach is applied to Bernoulli trials and
outperforms Akaike weights model averaging and post-model selection estimators.
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