Non‐parametric identification and estimation of the number of components in multivariate mixtures
Non‐parametric identification and estimation of the number of components in multivariate mixtures
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DOI：
10.1111/rssb.12022
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发表时间：
2014-01
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影响因子：
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通讯作者：
Hiroyuki Kasahara;Katsumi Shimotsu
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文献类型：
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作者：
Hiroyuki Kasahara;Katsumi Shimotsu
分析了k元M分量有限混合模型的分量个数的可辨识性，其中每个分量分布具有独立的边缘，包括潜在类分析中的模型。在不对分量分布进行参数假设的情况下，我们研究了如何从观测数据的分布函数中识别分量的数量。当k≥2时，分量数(M)的下界是非参数可从由观测变量的分布函数构造的矩阵的秩来识别的。在此识别条件的基础上，我们开发了一种程序，以一致地估计组件数量的下限。
We analyse the identifiability of the number of components in k‐variate, M‐component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k≥2, a lower bound on the number of components (M) is non‐parametrically identifiable from the rank of a matrix constructed from the distribution function of the observed variables. Building on this identification condition, we develop a procedure to estimate a lower bound on the number of components consistently.