Revisiting Tests for Neglected Non linearity Using Artificial Neural Networks
Revisiting Tests for Neglected Non linearity Using Artificial Neural Networks
复制标题
DOI：
10.1162/neco_a_00117
复制
发表时间：
2011-05-01
影响因子：
2.9
通讯作者：
White, Halbert
中科院分区：
文献类型：
--
作者：
Cho, Jin Seo;Ishida, Isao;White, Halbert
目前研究的基于人工神经网络的回归忽略非线性检验方法，主要是分别分析回归线性零点成立的两种方式。这意味着一般基于人工神经网络的被忽略非线性检验的渐近性仍然是一个悬而未决的问题。在这里，我们分析了一种方便的基于人工神经网络的准似然比统计量，用于检测被忽略的非线性，并仔细注意零的两个组成部分。分别导出了各分量下的渐近零分布，并分析了它们之间的相互作用。值得注意的是，对于类型1的情况，先前已知的渐近零分布仍然适用，但在比先前认识到的更强的条件下。我们提出了蒙特卡罗实验来证实我们的理论结果，并表明当我们的新的、更强的正则性条件被违反时，标准方法可能产生误导性的推断。
Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.