Abstract
This paper deals with some problems of eigenvalues and eigenvectors of a sample correlation matrix and derives the limiting distributions of their jackknife statistics with some numerical examples.
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References
Bellman R. (1960). Introduction to Matrix Analysis, McGraw-Hill, New York.
Beran R. (1984). Jackknife approximations to bootstrap estimates, Ann. Statist., 12, 101–118.
Beran R. and Srivastava M. S. (1985). Bootstrap tests and confidence regions for functions of a covariance matrix, Ann. Statist., 13, 95–115.
Fang C. and Krishnaiah P. R. (1982). Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations, J. Multivariate Anal., 12, 39–63.
Goto M. and Tazaki T. (1978). Methods of jackknife inference, Quality and Control., 8, 120–129 (in Japanese).
Hinkley D. V. (1978). Improving the jackknife with special reference to correlation estimation, Biometrika, 65, 13–21.
Konishi S. (1979). Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in principal component analysis, Hiroshima Math. J., 9, 647–700.
Lawley D. N. (1963). On testing a set of correlation coefficients for equality, Ann. Math. Statist., 34, 149–151.
Miller R. G.Jr. (1974). The jackknife: a review, Biometrika, 61, 1–15.
Nagao H. (1985). On the limiting distributions of the jackknife statistics for eigenvalues of a sample covariance matrix, Comm. Statist. A—Theory Methods, 14, 1547–1567.
Parr W. C. and Schucany W. R. (1980). The jackknife: a bibliography, Internat. Statist. Rev., 48, 73–78.
Rao C. R. (1964). The use and interpretation of principal component analysis in applied research, Sankhyā Ser. A, 26, 329–358.
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Nagao, H. On the jackknife statistics for eigenvalues and eigenvectors of a correlation matrix. Ann Inst Stat Math 40, 477–489 (1988). https://doi.org/10.1007/BF00053060
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DOI: https://doi.org/10.1007/BF00053060