Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods
Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods
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DOI：
10.1007/s11071-012-0576-y
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发表时间：
2012-09
影响因子：
5.6
通讯作者：
Pan Qin;R. Nishii;Zi‐Jiang Yang
中科院分区：
文献类型：
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作者：
Pan Qin;R. Nishii;Zi‐Jiang Yang
研究了具有外生变量的非线性自回归模型的加权最小二乘估计问题。由于WLS改变了研究数据的统计特性，违反了成熟的模型评估和选择方法（例如Akaike的信息准则，施瓦茨的贝叶斯信息准则和基于误差减少率的方法）的假设，因此，应该研究新的方法。在这项研究中，基于信息准则的方法和两个1-范数正则化方法被考虑：（a）在前一种方法中，对于使用WLS估计的模型，我们首先根据广义信息准则（GIC，由Konishi和Kitagawa在Biometrica 83（4）：875-890，1996中提出）导出信息准则，这是通过统计泛函方法分析和扩展信息准则的理论框架。（B）在后两种方法中，我们使用了1-范数正则化方法，包括Lasso和自适应Lasso，来选择WLS估计的模型。最后通过一个数值算例对三种方法的性能进行了测试和比较。
We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike’s information criterion, Schwarz’s Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and twol1-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875–890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwise method with Subsampling; (b) in the latter two methods, we employ thel1-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.