Testing equality of a large number of densities under mixing conditions
Testing equality of a large number of densities under mixing conditions
复制标题
在混合条件下测试大量密度的相等性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Hart
中科院分区：
文献类型：
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作者：
Marta Cousido‐Rocha;J. de Uña;J. Hart
在某些设置中，例如微阵列数据，采样信息由大量可能相互依赖的小数据集构成。在特殊的应用中，例如为了进行聚类，研究者的目的是验证所有的数据集是否具有共同的分布。出于这个原因，我们提出了零假设的正式检验，即所有数据集都来自单一分布。渐近设置是指小数据集的数量趋于无穷大，而样本量保持不变。在小数据集序列的混合条件下，导出了该检验的渐近零分布，并研究了该检验在两种合理的固定替代方案下的幂函数性质。仿真研究表明，该测试符合标称水平，且当数据集数量趋于无穷大时，其幂次趋于1。提供了一个涉及微阵列数据的说明。
In certain settings, such as microarray data, the sampling information is formed by a large number of possibly dependent small data sets. In special applications, for example in order to perform clustering, the researcher aims to verify whether all data sets have a common distribution. For this reason we propose a formal test for the null hypothesis that all data sets come from a single distribution. The asymptotic setting is that in which the number of small data sets goes to infinity, while the sample size remains fixed. The asymptotic null distribution of the proposed test is derived under mixing conditions on the sequence of small data sets, and the power properties of our test under two reasonable fixed alternatives are investigated. A simulation study is conducted, showing that the test respects the nominal level, and that it has a power which tends to 1 when the number of data sets tends to infinity. An illustration involving microarray data is provided.