# Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations

@inproceedings{Ma2021SampleCC, title={Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations}, author={Zongming Ma and Fan Yang}, year={2021} }

Consider two random vectors r x “ A z ` C 1 { 2 1 x P R p and r y “ B z ` C 1 { 2 2 y P R q , where x P R p , y P R q and z P R r are independent random vectors with i.i.d. entries of zero mean and unit variance, C 1 and C 2 are p ˆ p and q ˆ q deterministic population covariance matrices, and A and B are p ˆ r and q ˆ r deterministic factor loading matrices. With n independent observations of r x and r y , we study the sample canonical correlations between them. Under the sharp fourth moment…

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## References

SHOWING 1-10 OF 56 REFERENCES

### Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices

- Mathematics
- 2004

AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome…

### On the distribution of the largest eigenvalue in principal components analysis

- Mathematics
- 2001

Let x (1) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x (1) is the largest principal component…

### No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

- Mathematics
- 1998

Let B n = (1/N)T n 1/2 X n X n *Tn 1/2 , where X n is n x N with i.i.d. complex standardized entries having finite fourth moment and T n 1/2 is a Hermitian square root of the nonnegative definite…

### Independence test for high dimensional data based on regularized canonical correlation coefficients

- Mathematics
- 2015

This paper proposes a new statistic to test independence between two high dimensional random vectors ${\mathbf{X}}:p_1\times1$ and ${\mathbf{Y}}:p_2\times1$. The proposed statistic is based on the…

### Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit

- Mathematics
- 2020

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### Isotropic local laws for sample covariance and generalized Wigner matrices

- Mathematics
- 2013

We consider sample covariance matrices of the form $X^*X$, where $X$ is an $M \times N$ matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that…

### High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis

- Mathematics
- 2017

In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension p and the sample size n are large. The results are given for the…

### Anisotropic local laws for random matrices

- Mathematics
- 2014

We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random…

### Tracy-Widom distribution for the edge eigenvalues of Gram type random matrices.

- Computer Science, Mathematics
- 2020

This paper proves that under (almost) sharp moment conditions and certain tractable regularity assumptions, the edge eigenvalues of non-spiked Gram type random matrices satisfy the Tracy-Widom distribution asymptotically.