摘要翻译：
多元正态分布的有限混合在统计遗传学和统计金融学等领域有着广泛的应用。测试多元正态混合模型中的组分数是一个长期的挑战，即使在测试同质性的最重要的情况下也是如此。本文针对一般的$M_0\geq_1$提出了$M_0$成分的零假设与$M_0+1$成分的替代假设的基于似然性的检验。对于异方差正态混合，我们提出了EM检验，并导出了EM检验统计量的渐近分布。对于同方差正态混合，我们导出了似然比检验统计量的渐近分布。我们还导出了局部方案下的似然比检验统计量和EM检验统计量的渐近分布，并证明了参数自举的有效性。仿真结果表明，该方法具有良好的有限样本量和功率特性。
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英文标题：
《Testing the Order of Multivariate Normal Mixture Models》
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作者：
Hiroyuki Kasahara and Katsumi Shimotsu
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture models is a long-standing challenge even in the most important case of testing homogeneity. This paper develops likelihood-based tests of the null hypothesis of $M_0$ components against the alternative hypothesis of $M_0 + 1$ components for a general $M_0 \geq 1$. For heteroscedastic normal mixtures, we propose an EM test and derive the asymptotic distribution of the EM test statistic. For homoscedastic normal mixtures, we derive the asymptotic distribution of the likelihood ratio test statistic. We also derive the asymptotic distribution of the likelihood ratio test statistic and EM test statistic under local alternatives and show the validity of parametric bootstrap. The simulations show that the proposed test has good finite sample size and power properties.
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PDF链接：
https://arxiv.org/pdf/1902.02920