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arXiv · 1707.04010

Testing High-dimensional Covariance Matrices under the Elliptical Distribution and Beyond

Xinxin Yang·Xinghua Zheng·Jiaqi Chen
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Abstract

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume specific parametric distributions nor involve the kurtosis of data. More generally, we can test against any non-negative definite matrix that can even be not invertible. As an interesting application, we illustrate in empirical studies that our tests can be used to test uncorrelatedness among idiosyncratic returns.

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Xinxin Yang, Xinghua Zheng, Jiaqi Chen. 2017-07-13. Testing High-dimensional Covariance Matrices under the Elliptical Distribution and Beyond. https://arxiv.org/abs/1707.04010

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