Some tests for the covariance matrix with fewer observations than the dimension under non-normality
Some tests for the covariance matrix with fewer observations than the dimension under non-normality
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DOI：
10.1016/j.jmva.2011.03.003
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
M. Srivastava;T. Kollo;D. Rosen
中科院分区：
文献类型：
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作者：
M. Srivastava;T. Kollo;D. Rosen
本文分析了现有的N个独立同分布观测向量的p× p协方差矩阵Σ的检验是否在非正态性下有效。我们专注于三个假设检验问题：（1）检验球度，即协方差矩阵n与单位矩阵I p成比例;（2）协方差矩阵n是单位矩阵I p;（3）协方差矩阵是对角矩阵。结果表明，Srivastava（2005）对上述三个问题提出的检验在本文所作的非正态性假设下是稳健的，无论N≤ p还是N≥ p，但（N，p）→∞，且N/p可能趋于零或无穷大。结果是渐近的，可以注意到，它们可能不适用于有限的（N，p）。
This article analyzes whether some existing tests for the p× p covariance matrix Σ of the N independent identically distributed observation vectors work under non-normality. We focus on three hypotheses testing problems:(1) testing for sphericity, that is, the covariance matrix Σ is proportional to an identity matrix I p;(2) the covariance matrix Σ is an identity matrix I p; and (3) the covariance matrix is a diagonal matrix. It is shown that the tests proposed by Srivastava (2005) for the above three problems are robust under the non-normality assumption made in this article irrespective of whether N≤ p or N≥ p, but (N, p)→∞, and N/p may go to zero or infinity. Results are asymptotic and it may be noted that they may not hold for finite (N, p).