In this paper https://www.sciencedirect.com/science/article/pii/S0167947307003957 it is shown how to build an estimator of the variance of estimates computed after variable selection.

It evaluates the variance in each competitive model adjusted for the bias of the estimate from average estimate, weighted by the "importance" of the model:

$$var(\hat{\theta}) = \sum_kw_k\sqrt{var(\hat{\theta}|M_k) + (\hat{\theta}_k - \hat{\theta})^2}$$

In my case, the competitive models are created by variables selection after bootstrapping the original dataset, in order to evaluate the variability of selection due to the data. the weights are given by the proportion of time a certain variable is included in the model.

My question is what to use as $n$ to build $s.e(\theta)=\sqrt{\frac{var(\hat{\theta})}{n}}$. Should I use the numerosity of the original dataset?


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