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
Vector Spaces and Matrices | 1 |
Linear Estimation | 29 |
Tests of Linear Hypotheses | 51 |
Singular Values and Their Applications | 79 |
Block Designs and Optimality | 99 |
Rank Additivity 113 | 112 |
Notes | 129 |
136 | |
Andra upplagor - Visa alla
Vanliga ord och fraser
applications assume assumptions basis block BLUE called Chapter characteristic choice Clearly column complete components conclude Consider contain Conversely correlation corresponding defined denote determinant diagonal distribution eigenvalues eigenvector entries equal equation estimable Exercise exists fact Find follows function g-inverse given hence holds idempotent identity inequality inverse Let A,B LetA linear combination linear model linearly independent matrix of rank maximum mean multiplicity nonsingular nonzero normal Note observations obtained orthogonal orthogonal matrix partitioned positive definite positive semidefinite possible Problems proof proved random rank rank factorization respectively result satisfies seen similar Similarly singular values solution span spectral statistic submatrix Suppose symmetric symmetric matrix theorem treatment true unique variables variance vector space verified write zero
Hänvisningar till den här boken
Matrix Algebra and Its Applications to Statistics and Econometrics Calyampudi Radhakrishna Rao,M. Bhaskara Rao Begränsad förhandsgranskning - 1998 |