On the sphericity test with large-dimensional observations

By Qinwen Wang, Jianfeng Yao. 2013

76 citations recorded by the source corpus.

In this paper, we propose corrections to the likelihood ratio test and John's test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c5b942fba735615368efe6ee33d6c07622f8e0f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jianfeng Yao
2. Clifford Lam
3. Qiwei Yao
4. Zeng Li
5. Shu-rong Zheng
6. Damien Passemier
7. Z. Li
8. Z. Bai

In Mathematical Physics

1. Jianfeng Yao
2. Zeng Li
3. Shu-rong Zheng
4. Z. Bai
5. Damien Passemier
6. Z. Li
7. Qiwei Yao
8. Clifford Lam

In Statistics and Probability

1. Jianfeng Yao
2. Clifford Lam
3. Zeng Li
4. Shu-rong Zheng
5. Qiwei Yao
6. Damien Passemier
7. Z. Li
8. Z. Bai

Citations in the corpus

• On estimation of the noise variance in high dimensional probabilistic principal component analysis (2013, background): “Proof of theorem 3 By lemma 2.2 of Wang and Yao (2013), we have Gn.x/= p∑ i=1 λn, i −p ∫ xdFcn ,Hn .x/ D→N{m.x/, v.x/}: The asymptotic mean does not change for non-Gaussian data, m.x/ = 0, but the asymptotic variance is v.x/= cγσ4.”
• Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing (2014, background): “(4.10) in Wang and Yao [22], we readily find the claimed formula for m∗N (g) and υ ∗ N (g).”
• On testing for high-dimensional white noise (2018, background): “Such high-dimensional traps for classical procedures have already been reported in other testing problems, see for example [4] and [39].”