Linear Algebra and Linear ModelsSpringer Science & Business Media, 2000 - 138 sidor The main purpose of Linear Algebra and Linear Modelsis to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms are developed along the way. The book is aimed at advanced undergraduate and first-year graduate masters students taking courses in linear algebra, linear models, multivariate analysis, and design of experiments. It should also be of use to research mathematicians and statisticians as a source of standard results and problems. |
Innehåll
Linear Estimation | 29 |
Tests of Linear Hypotheses | 51 |
4 | 60 |
6 | 67 |
9 | 76 |
Block Designs and Optimality | 99 |
Rank Additivity | 115 |
Notes | 129 |
136 | |
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basis BIBD block BLUE C-matrix Chapter column rank column vector Consider the model correlation defined denote diagonal dim(T dispersion matrix eigenvalues eigenvector equal Exercise F-statistic GA)z given group inverse Hadamard Hadamard inequality Hadamard matrix hence Hint idempotent inequality j)-entry least squares g-inverse Linear Algebra linear combination linear model linear span linearly independent matrices of order matrix and let matrix of rank minimum norm g-inverse Mitra model E(y Moore–Penrose inverse multiplicity nonsingular matrix nonzero orthogonal matrix orthonormal partitioned positive definite positive semidefinite matrix principal component principal minors principal submatrix proof is complete R(AB rank factorization real numbers row space RSSH Schur complement Similarly singular values solution spectral theorem square matrix star order submatrix subspace Suppose symmetric matrix variables variance vector space verified Xẞ y₁ zero
Hänvisningar till den här boken
Matrix Algebra and Its Applications to Statistics and Econometrics Calyampudi Radhakrishna Rao,M. Bhaskara Rao Begränsad förhandsgranskning - 1998 |