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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국자료분석학회 Journal of The Korean Data Analysis Society Journal of The Korean Data Analysis Society 제7권 제1호
- 발행연도
- 2005.1
- 수록면
- 81 - 87 (7page)
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In this paper we consider the simultaneous diagonalization of two positive definite matrices. A necessary and sufficient condition is found under which two positive definite covariance matrices are simultaneously diagonalized in view of a Cholesky decomposition. This result can be applied to estimating the eigenvalues and eigenvectors of for two positive definite covariance matrices ,. under multivariate normality. The result is extended to more than two matrices. The result is also applied to computing the conditional expectations contained in some decompositions of the Mahalanobis distance that help us to explain some reasons for the outlyingness of multivariate observations in multivariate analysis. Since the Cholesky decomposition of covariance matrix is useful in expressing the conditional expectation of one variable when the remaining variables are fixed under multivariate normality. An example is given for an illustration.
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참고문헌 (11)
참고문헌 신청
/ 1969 / Introduction to matrices with applications in statistics
/ 1982 / Aspects of multivariate Statistical Theory
/ 1982191-198 / The Cholesky factorization of the inverse correlation or covariance matrix in multiple regression tech (metrics)
/ 1984 / Common principal components analysis 79 : 892 ~ 898
/ 1985 / Estimating a Cholesky decomposition 67 : 201 ~ 205
/ 1982 / Aspects of multivariate Statistical Theory
/ 1982191-198 / The Cholesky factorization of the inverse correlation or covariance matrix in multiple regression tech (metrics)
/ 1984 / Common principal components analysis 79 : 892 ~ 898
/ 1985 / Estimating a Cholesky decomposition 67 : 201 ~ 205
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