On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

Y. Q. Yin; Z. D. Bai; P. R. Krishnaiah

doi:10.1007/bf00353874

journal article Aug 01, 1988

On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

Y. Q. Yin Z. D. Bai P. R. Krishnaiah

Probability Theory and Related Fields Vol. 78 No. 4 pp. 509-521 · Springer Science and Business Media LLC

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References

16

[1]

Bai, Z.D., Silverstein, J., Yin, Y.Q.: A note on the largest eigenvalue of a large dimensional sample covariance matrix. Technical Report No. 86-29, Center for Multivariate Analysis, University of Pittsburgh (1986) to appear in J. Multivariate Anal.

[2]

Bai, Z.D., Yin, Y.Q.: Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Probab. Th. Rel. Fields 73, 555–569 (1986) 10.1007/bf00324852

[3]

Bai, Z.D., Yin, Y.Q., Krishnaiah, P.R.: On limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Teoriya Veroyatnostei i ee Primeneniya (Theory of Probability and its Applications: English translation published by SIAM) 32, 537–548 (1987)

[4]

Bai, Z.D., Yin, Y.Q., Krishnaiah, P.R.: On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. J. Multivariate Anal. 19, 189–200 (1986) 10.1016/0047-259x(86)90103-x

[5]

Geman, S.: A limit theorem for the norm of random matrices. Ann. Probab. 8, 252–261 (1980)

[6]

Grenander, U., Silverstein, J.: Spectral analysis of networks with random topologies. SIAM J. Appl. Math. 32 (2), 499–519 (1977) 10.1137/0132041

[7]

Jonsson, D.: Some limit theorems for the eigenvalues of a sample covariance matrix. J. Multivariate Anal. 12, 1–38 (1982) 10.1016/0047-259x(82)90080-x

[8]

Jonsson, D.: On the largest eigenvalues of sample covariance matrix. In: Krishnaiah, P.R. (ed.) Multivariate Analysis VI. North-Holland 1983

[9]

Silverstein, J.: On the largest eigenvalues of a large dimensional sample covariance matrix. Unpublished manuscript (1984)

[10]

Wachter, K.W.: The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab. 6, 1–18 (1978) 10.1214/aop/1176995607

[11]

Wachter, K.W.: The limiting empirical measure of multiple discriminant ratios. Ann. Statist. 8, 937–957 (1980) 10.1214/aos/1176345134

[12]

Yin, Y.Q.: Limit spectral distribution for a class of random matrices. J. Multivariate Anal. 20, 50–68 (1986) 10.1016/0047-259x(86)90019-9

[13]

Yin, Y.Q., Bai, Z.D., Krishnaiah, P.R.: Limiting behavior of the eigenvalues of a multivariate F matrix. J. Multivariate Anal. 13, 508–516 (1983) 10.1016/0047-259x(83)90036-2

[14]

Yin, Y.Q., Krishnaiah, P.R.: Limit theorems for the eigenvalues of product of two random matrices. J. Multivariate Anal. 13, 489–507 (1983) 10.1016/0047-259x(83)90035-0

[15]

Yin, Y.Q., Krishnaiah, P.R.: Limit theorems for the eigenvalues of the sample covariance matrix when the underlying distribution is isotropic. Teoriya Veroyatnostei i ee Primeneniya (Theory of Probability and its Applications: English translation published by SIAM) 30, 810–816 (1986a)

[16]

Yin, Y.Q., Krishnaiah, P.R.: Limit theorems for the eigenvalues of product of two large dimensional random matrices when the underlying distribution is isotropic. Teoriya Veroyatnostei i ee Primeneniya (Theory of Probability and its Applications: English translation published by SIAM) 31, 394–398 (1986b)

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Published: Aug 01, 1988
Vol/Issue: 78(4)
Pages: 509-521
License: View

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Cite This Article

Y. Q. Yin, Z. D. Bai, P. R. Krishnaiah (1988). On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Probability Theory and Related Fields, 78(4), 509-521. https://doi.org/10.1007/bf00353874

On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

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