ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX

By Z. Bai, Jiaqi Chen, Jianfeng Yao. 2010

59 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e262f05b889ed3cdc002754d92e12473704c6028

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. Xinghua Zheng
2. Yingying Li
3. Damien Passemier
4. Z. Li
5. Guangming Pan
6. Zeng Li
7. Yanrong Yang
8. Debashis Paul

In Statistics and Probability

1. Clifford Lam
2. Jianfeng Yao
3. Zeng Li
4. Qiwei Yao
5. Alexander Aue
6. Debashis Paul
7. Guangming Pan
8. Damien Passemier

Citations in the corpus

• Independence test for high dimensional data based on regularized canonical correlation coefficients (2015, background): “Indeed, Theorem 1 of [3] implies that the best possible convergence rate is Op( 1 n).”
• On the estimation of integrated covariance matrices of high dimensional diffusion processes (2010, methodology): “This is because, if we let Z̃ be the result of replacing Z(p,j) , j ∈ Ip, with independent random variables with the same distribution that are also independent of w , and S̃ := ∑n =1 w · 1/2Z̃ (Z̃ )T 1/2, then rank(S̃ − S) ≤ 2ηp , and so by the rank inequality ‖FA − FB‖ ≤ rank(A − B) p for any A,B ”
• Random matrix theory in statistics: A review (2014, background): “Bai et al. (2009) and Bai et al. (2010) used Bernstein polynomial approximation for g, which is now required to be only four times continuously differentiable, to extend the results in Bai and Silverstein (2004) on the CLT of (24) for Wigner and Wishart matrices, respectively.”
• 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 Bai et al. (2009) and Wang and Yao (2013).”
• On estimation of the noise variance in high dimensional probabilistic principal component analysis (2013, methodology): “;Hn (x) ! ND (m(x);v(x)), 31 with asymptotic mean m(x) = 0 ; (16) and asymptotic variance v(x) = 2c˙4 : (17) The derivation of these two formula are given in the Section 6. Furthermore, by Lemma 1 of Bai et al. (2010), Z xdF cn;Hn (x) = Z tdH n(t) = ˙2 + 1 p Xm i=1 i. So we have Xp i=1 n;i p˙2 Xm i”