다변량 통계분석 중간고사 기말고사 기출문제
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- 2023.06.08
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- 2017.03
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본문내용
A. (2 points each) True (O) or False (X)?
(1) The sum of the eigenvalues of a square matrix A equals tr(A) and the product of the eigenvalues equals jAj.
(2) If a matrix A has eigenvectors e1; ; ep with eigenvalues 1; ; p, then I+A has the same eigenvectors with eigenvalues 1 + 1; ; p + 1.
(3) is positive denite.
(4) If X1;X2 and X3 have univariate normal distributions marginally, then (X1;X2;X3)0 has a multivariate normal distribution.
(5) If W1 and W2 are independent Wishart(p;m1;) and Wishart(p;m2;), then W1 +W2 have a Wishart(p;m1 + m2;) distribution.
(6) If X = (X1;X2;X3;X4)0 has a multivariate normal distribution, then (X1;X3)0 given (X2;X4)0 = (1; 2)0 has a bivariate normal distribution.
(7) tr
(8) Hotelling's T2 test for a multivariate normal mean is equivalent to the likelihood ratio test for the multivariate normal mean.
(9) Bonferroni's simultaneous condence intervals can be obtained by projecting the condence ellipsoid of Hotelling's T2.
참고 자료
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