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Variable selection and estimation for high-dimensional spatial autoregressive models

机译:高维空间自回归模型的可变选择与估算

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Spatial regression models are important tools for many scientific disciplines including economics, business, and social science. In this article, we investigate postmodel selection estimators that apply least squares estimation to the model selected by penalized estimation in high-dimensional regression models with spatial autoregressive errors. We show that by separating the model selection and estimation process, the postmodel selection estimator performs at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence. Moreover, under perfect model selection, the l(2) rate of convergence is the oracle rate of root s/n, comparedwith the convergence rate of root s log p/n in the general case. Here, n is the sample size and p, s are the model dimension and number of significant covariates, respectively. We further provide the convergence rate of the estimation error in the form of sup v norm, and ideally the rate can reach as fast as root log s/n.
机译:空间回归模型是许多科学学科的重要工具,包括经济学,商业和社会科学。在本文中,我们调查了将最小二乘估计应用于在具有空间自回归误差的高维回归模型中所选择的模型中应用最小二乘估计。我们表明,通过分离模型选择和估计过程,后模型选择估计器至少在收敛速率方面执行和同时可变选择和估计方法。此外,在完美的模型选择下,L(2)的收敛速率是根S / N的Oracle率,与常规外壳中的根目录P / N的收敛速率相比。这里,n是样本大小,p,s分别是模型尺寸和大量协变量的数量。我们进一步提供了SUP V规范形式的估计误差的收敛速度,理想情况下,速率可以达到作为root log s / n的快速。

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