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Abstract:
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E-MS algorithm associates the idea of E-M algorithm with model selection in the presence of missing data. The idea extends the concept of parameters to include both the model and the parameters under the model, and thus allows the model to be part of the E-M iterations. We propose new inference procedure for the final model selected by E-MS algorithm. Under the assumptions of Gaussian responses and a finite class of candidate models, we propose a bootstrap procedure that resamples the original data many times and keep only those samples for which the sequence of selected models is the same as that obtained in original data to estimate the variance-covariance matrix for coefficients of final E-MS model, instead of basing it on the naive Hessian matrix. This strategy is motivated by the post-selective inference ideas recently appearing in the literature. In our simulations, the new procedure works much better even for a relatively small number of bootstrap samples. We also study the theoretical properties of the inferential procedure, which in turn indicates the validity of new method.
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