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Abstract:
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In this work, we investigate post-model selection estimators that apply least squares estimation to the model selected by first-step penalized estimation in high dimensional regression model with spatial autoregressive errors. The unknown spatial autoregressive parameters are estimated using generalized moment estimators and then 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. 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 l-2 convergence rate is the oracle rate compared to convergence rate in the general penalized estimation situation. We further provide the convergence rate of the estimation error in the form of sup norm when the model selection process perfectly selects the true model. All the theoretical results are validated by simulation studies in comparison with the simultaneous variable selection and estimation methods.
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