Approximations to the distribution of the sample correlation matrix

Journal of Multivariate Analysis

Volumn 85, Issue 2, 2003, Pages 318-334

  Kollo, Tõnu ^a   Ruul, Kaire ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

Characteristic function of random matrix; Matrix derivative; Multivariate cumulants; Multivariate density approximation; Multivariate Taylor expansion

Indexed keywords

EID: 0038511255     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00037-4     Document Type: Article

References (13)

1. T.W. Anderson, Introduction to Multivariate Statistical Analysis, 2nd Edition, Wiley, New York, 1984.
2. R.J. Boik, A local parameterization of orthogonal and semi-orthogonal matrices with applications, J. Multivariate Anal. 67 (1998) 244-276.
3. R.A. Fisher, Frequency distribution of the values of the correlation coefficient in samples from an infinitely large population, Biometrika 10 (1915) 507-521.
4. M.A. Girshick, On the sampling theory of roots of determinantal equations, Ann. Math. Statist. 10 (1939) 203-224.
5. B. Holmquist, The d-variate vector Hermite polynomial of order k, Linear Algebra Appl. 237/238 (1996) 155-190.
6. T. Kollo, On the correspondence between matrix derivative and some basic notions of multivariate statistics, Tartu Ül. Toimetised 942 (1992) 28-34.
7. T. Kollo, H. Neudecker, Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices, J. Multivariate Anal. 47 (1993) 283-300.
8. T. Kollo, D. von Rosen, Approximating by the Wishart distribution, Ann. Inst. Statist. Math. 47 (1995) 767-783.
9. T. Kollo, D. von Rosen, A unified approach to the approximation of multivariate densities, Scand. J. Statist. 25 (1998) 93-109.
10. J. Magnus, H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition, Wiley, Chichester, 1999.
11. H. Neudecker, A.M. Wesselmann, The asymptotic variance matrix of the sample correlation matrix, Linear Algebra Appl. 127 (1990) 589-599.
12. A.-M. Parring, Calculation of asymptotic characteristics of sample functions, Tartu Riikl. Ül. Toimetised 492 (1979) 82-90 (in Russian).
13. C.R. Rao, Linear Statistical Inference and Its Applications, 2nd Edition, Wiley, New York, 1973.