Linear Algebra and Linear ModelsSpringer Science & Business Media, 18 jan. 2008 - 139 sidor This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians. |
Innehåll
EigenvaluesandtheSpectralTheorem | 27 |
Tests of Linear Hypotheses | 51 |
ResidualSumofSquares | 73 |
4 | 79 |
5 | 99 |
Rank Additivity 113 | 112 |
14 | 119 |
Notes | 129 |
| 134 | |
| 136 | |
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ABTA BIBD block C-matrix Chapter chi-square Consider the model d e TXv D-optimality defined denote diagonal dispersion matrix eigenvalues eigenvector equal Exercise exists F-statistic given group inverse Hadamard inequality hence Hint idempotent inequality least squares g-inverse Let A,B Let X1 linear combination linear model linear span linearly independent m x n matrices of order matrix and let matrix of rank maximum minimum norm g-inverse Moore–Penrose inverse multiplicity multivariate normal distribution n x n matrix nonsingular nonzero normal equations observations orthogonal matrix orthonormal partitioned positive semidefinite matrix principal component principal minors principal submatrix proof is complete rank factorization real numbers result is proved row space RSSH Schur complement Similarly singular values spectral theorem square matrix star order submatrix subspace Suppose symmetric matrix treatment u'Au variance VC1V vector space verified zero