Multimodality of the likelihood in the bivariate seemingly unrelated regressions model
Multimodality of the likelihood in the bivariate seemingly unrelated regressions model
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DOI：
10.1093/biomet/91.2.383
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发表时间：
2004-06-01
期刊：
影响因子：
2.7
通讯作者：
Richardson, TS
中科院分区：
文献类型：
--
作者：
Drton, M;Richardson, TS
我们分析了最简单的两方程看似无关的回归模型，并证明其可能性可能有多达五个平稳点，因此可能有多达三个本地模式。因此，通过迭代估计方法获得的估计可能取决于起始值。我们进一步表明，多模态的概率渐近消失。蒙特卡罗模拟表明，如果看似不相关的回归模型是真的，多模态很少发生，但如果模型被错误指定，则可能会变得更频繁。看似无关的回归模型的可能性的多峰性的存在与文献中的几个主张相矛盾。
We analyse the simplest two-equation seemingly unrelated regressions model and demonstrate that its likelihood may have up to five stationary points, and thus there may be up to three local modes. Consequently the estimates obtained via iterative estimation methods may depend on starting values. We further show that the probability of multi-modality vanishes asymptotically. Monte Carlo simulations suggest that multimodality rarely occurs if the seemingly unrelated regressions model is true, but can become more frequent if the model is misspecified. The existence of multimodality in the likelihood for seemingly unrelated regressions models contradicts several claims in the literature.