Higher-Order Approximations for Testing Neglected Nonlinearity
Higher-Order Approximations for Testing Neglected Nonlinearity
复制标题
用于测试被忽略的非线性的高阶近似
DOI：
10.1162/neco_a_00225
复制
发表时间：
2012
影响因子：
2.9
通讯作者：
J. Cho
中科院分区：
文献类型：
--
作者：
H. White;J. Cho
我们说明了需要使用高阶（特别是六阶）的扩展，以正确地确定被忽略的非线性的标准人工神经网络测试的渐近分布。检验统计量是一种准似然比（QLR）统计量，旨在检验均方预测误差是否通过包括具有违反Cho，Ishida和白色（2011）中的非零条件的激活函数的额外隐藏单元而得到改善。这个统计量也被证明在零下渐近等价于Luukkonen，Saikkonen，and Teräsvirta（1988）和Teräsvirta（1994）的拉格朗日乘子（LM）统计量。此外，我们比较我们的QLR测试的功率特性，一个满足无零条件，并发现后者是不一致的检测DGP忽略非线性违反类似的无零条件，而我们的QLR测试是一致的。
We illustrate the need to use higher-order (specifically sixth-order) expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity. The test statistic is a quasi-likelihood ratio (QLR) statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activation function violating the no-zero condition in Cho, Ishida, and White (2011). This statistic is also shown to be asymptotically equivalent under the null to the Lagrange multiplier (LM) statistic of Luukkonen, Saikkonen, and Teräsvirta (1988) and Teräsvirta (1994). In addition, we compare the power properties of our QLR test to one satisfying the no-zero condition and find that the latter is not consistent for detecting a DGP with neglected nonlinearity violating an analogous no-zero condition, whereas our QLR test is consistent.