Optimal detection of heterogeneous and heteroscedastic mixtures
Optimal detection of heterogeneous and heteroscedastic mixtures
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DOI：
10.1111/j.1467-9868.2011.00778.x
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发表时间：
2011-01-01
影响因子：
5.8
通讯作者：
Jin, Jiashun
中科院分区：
文献类型：
--
作者：
Cai, T. Tony;Jeng, X. Jessie;Jin, Jiashun
研究了非均匀和异方差高斯混合的检测问题。重点讨论了异质性、异方差和非零分量比例等参数对问题难易程度的影响。我们建立了一个明确的检测边界，将似然比检验显示可以可靠地检测非零效应的可检测区域与无法检测的区域分开，其中没有方法可以这样做。结果表明，当非零分量的比例从稀疏区转移到稠密区时，检测边界发生了显著变化。此外，研究表明，不需要模型参数的特定信息的高批评检验在稀疏和密集情况下都能最优地适应未知程度的异质性和异方差。
The problem of detecting heterogeneous and heteroscedastic Gaussian mixtures is considered. The focus is on how the parameters of heterogeneity, heteroscedasticity and proportion of non-null component influence the difficulty of the problem. We establish an explicit detection boundary which separates the detectable region where the likelihood ratio test is shown to detect the presence of non-null effects reliably from the undetectable region where no method can do so. In particular, the results show that the detection boundary changes dramatically when the proportion of non-null component shifts from the sparse regime to the dense regime. Furthermore, it is shown that the higher criticism test, which does not require specific information on model parameters, is optimally adaptive to the unknown degrees of heterogeneity and heteroscedasticity in both the sparse and the dense cases.