Testing the Number of Components in Normal Mixture Regression Models
Testing the Number of Components in Normal Mixture Regression Models
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DOI：
10.1080/01621459.2014.986272
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发表时间：
2015-10
影响因子：
3.7
通讯作者：
Hiroyuki Kasahara;Katsumi Shimotsu
中科院分区：
文献类型：
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作者：
Hiroyuki Kasahara;Katsumi Shimotsu
由于其非规则性，测试有限正态混合模型中的组件数量是一个长期存在的挑战。本文研究了具有异方差成分的正态混合回归模型中成分数量的基于可能性的检验。我们针对任何 m0 的 m0 分量的原假设与 m0 + 1 分量的备择假设构建基于似然的检验。所提出的修正 EM 检验统计量的零渐近分布是可以轻松模拟的 m0 个随机变量的最大值。模拟表明，所提出的测试具有非常好的有限样本大小和功效特性。本文的补充材料可在线获取。
Testing the number of components in finite normal mixture models is a long-standing challenge because of its nonregularity. This article studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of m0 components against the alternative hypothesis of m0 + 1 components for any m0. The null asymptotic distribution of the proposed modified EM test statistic is the maximum of m0 random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties. Supplementary materials for this article are available online.