Regression coefficient and autoregressive order shrinkage and selection via the lasso
Regression coefficient and autoregressive order shrinkage and selection via the lasso
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DOI：
10.1111/j.1467-9868.2007.00577.x
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
Hansheng Wang;Guodong Li;Chih-Ling Tsai
中科院分区：
文献类型：
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作者：
Hansheng Wang;Guodong Li;Chih-Ling Tsai
概括。最小绝对收缩和选择算子（‘lasso’）已广泛用于回归收缩和选择。我们将其应用扩展到具有自回归误差的回归模型。仔细研究了两种类型的套索估计器。第一个类似于传统的套索估计器，只有两个调整参数（一个用于回归系数，另一个用于自回归系数）。这些调整参数可以通过数据驱动的方法轻松计算，但所得的套索估计器可能并不完全有效。为了克服这个限制，我们提出了第二个套索估计器，它对每个系数使用不同的调整参数。我们证明，这种修改后的套索可以像预言机一样高效地生成估计器。此外，我们提出了一种调整参数估计的算法以获得修改后的套索估计器。仿真研究表明，改进的估计器优于传统的估计器。还提出了一个实证示例来说明套索估计器的有用性。简要讨论了套索对外生变量自回归模型的推广。
Summary. The least absolute shrinkage and selection operator (‘lasso’) has been widely used in regression shrinkage and selection. We extend its application to the regression model with autoregressive errors. Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients and the other for autoregression coefficients). These tuning parameters can be easily calculated via a data‐driven method, but the resulting lasso estimator may not be fully efficient. To overcome this limitation, we propose a second lasso estimator which uses different tuning parameters for each coefficient. We show that this modified lasso can produce the estimator as efficiently as the oracle. Moreover, we propose an algorithm for tuning parameter estimates to obtain the modified lasso estimator. Simulation studies demonstrate that the modified estimator is superior to the traditional estimator. One empirical example is also presented to illustrate the usefulness of lasso estimators. The extension of the lasso to the autoregression with exogenous variables model is briefly discussed.