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Abstract:
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In this paper, we investigate post-model selection estimators that apply least squares estimation to the model selected by first-step penalized estimation in the high dimensional regression model with spatial autoregressive errors. The unknown spatial autoregressive parameter in the model is estimated using generalized moments estimator and can then be treated as a nuisance parameter. We show that by separating the model selection and estimation process, the post-model selection estimator can perform at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence (including both L2 and sup norm). Moreover, under perfect model selection, that is, when the selection process is able to correctly identify the significant covariates of the true model with probability goes to 1, the rate of convergence will be strictly better. All the theoretical results are validated by simulation studies in comparison with the simultaneous variable selection and estimation methods.
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