Asymptotic expansion of the sample correlation coefficient under nonnormality

Computational Statistics and Data Analysis

Volumn 50, Issue 4, 2006, Pages 891-910

  Ogasawara, Haruhiko ^a  

^a OTARU UNIVERSITY OF COMMERCE   (Japan)

Author keywords

Correlation coefficient; Edgeworth expansion; Fourth cumulants; Nonnormality

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; ERROR ANALYSIS; FUNCTIONS; VARIATIONAL TECHNIQUES;

CORRELATION COEFFICIENT; EDGEWORTH EXPANSION; FOURTH CUMULANTS; NONNORMALITY;

CORRELATION METHODS;

EID: 26444589703     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2004.11.001     Document Type: Article

References (30)

1. T.W. Anderson An Introduction to Multivariate Statistical Analysis second ed 1984 Wiley New York
2. R.J. Boik A local parameterization of orthogonal and semi-orthogonal matrices with applications J. Multivariate Anal. 67 1998 244 276
3. M.W. Browne, and A. Shapiro The asymptotic covariance matrix of sample correlation coefficients under general conditions Linear Algebra Appl. 82 1986 169 176
4. R.A. Fisher Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population Biometrika 10 1915 507 521
5. R.A. Fisher On the "probable error" of a coefficient of correlation deduced from a small sample Metron 1 1921 3 32
6. Y. Fujikoshi Asymptotic expansions for the distributions of the sample roots under nonnormality Biometrika 67 1980 45 51
7. M.A. Girshick On the sampling theory of roots of determinantal equations Ann. Math. Statist. 10 1939 203 224
8. Hall, P., 1992. The Bootstrap and Edgeworth Expansion. Springer, New York, Corrected printing, 1997.
9. H. Hotelling New light on the correlation coefficient and its transforms (with discussion) J. Roy. Statist. Soc. Ser. B 15 1953 193 232
10. P.L. Hsu The limiting distribution of functions of sample means and application to testing hypotheses J. Neyman Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability 1949 University of California Press Berkeley 359 402
11. N.L. Johnson, and S. Kotz Continuous Univariate Distributions-1 1970 Wiley New York
12. E.L. Kaplan Tensor notation and the sampling cumulants of k-statistics Biometrika 39 1952 319 323
13. T. Kollo, and K. Ruul Approximations to the distribution of the sample correlation matrix J. Multivariate Anal. 85 2003 318 334
14. S. Konishi An approximation to the distribution of the sample correlation coefficient Biometrika 65 1978 654 656
15. S. Konishi Asymptotic expansions for the distributions of functions of a correlation matrix J. Multivariate Anal. 9 1979 259 266
16. S. Konishi Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in principal component analysis Hiroshima Math. J. 9 1979 647 700
17. D.G. Nel A matrix derivation of the asymptotic covariance matrix of sample correlation coefficients Linear Algebra Appl. 67 1985 137 145
18. H. Neudecker The asymptotic variance matrices of the sample correlation matrix in elliptical and normal situations and their proportionality Linear Algebra Appl. 237-238 1996 127 132
19. H. Neudecker, and A.M. Wesselman The asymptotic variance matrix of the sample correlation matrix Linear Algebra Appl. 127 1990 589 599
20. N. Niki, and S. Konishi Higher order asymptotic expansions for the distribution of the sample correlation coefficient Comm. Statist. - Simul. Comput. 13 1984 169 182
21. Ogasawara, H., 2004a. Asymptotic biases in exploratory factor analysis and structural equation modeling. Psychometrika, in press.
22. Ogasawara, H., 2004b. Higher-order estimation error in factor analysis and structural equation modeling, submitted for publication.
23. Ogasawara, H., 2004c. Asymptotic expansion in factor analysis and structural equation modeling under normality and nonnormality, submitted for publication.
24. I. Olkin, and J.W. Pratt Unbiased estimation of certain correlation coefficients Ann. Math. Statist. 29 1958 201 211
25. I. Olkin, and M. Siotani Asymptotic distribution of functions of a correlation matrix S. Ikeda Essays in Provability and Statistics A Volume in Honour of Professor Junjiro Ogawa 1976 Shinko Tsusho Tokyo 235 251
26. K. Pearson, and L.N.G. Filon Mathematical contributions to the theory of evolution.-IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation Philos. Trans. Roy. Soc. London Ser. A Math. Phys. Sci. 191 1898 229 311
27. E.J.G. Pitman Significance tests which may be applied to samples from any populations. II The correlation coefficient test. J. Roy. Statist. Soc. 4 Suppl. 1937 225 232
28. J.H. Steiger, and A.R. Hakstian The asymptotic distribution of elements of a correlation matrix theory and application British J. Math. Statist. Psychol. 35 1982 208 215
29. J.H. Steiger, and A.R. Hakstian A historical note on the asymptotic distribution of correlations British J. Math. Statist. Psychol. 36 1983 157
30. Stuart, A., Ord, J.K., 1994. Kendall's Advanced Theory of Statistics: Distribution Theory, sixth ed., vol. 1. Arnold, London.