Mathematics for Econometrics
The book also covers psuedo-inverses, solutions to systems of linear equations, solutions of vector difference equations with constant coefficients and random forcing functions, matrix differentiation, and permutation matrices. Its novel features include an introduction to asymptotic expansions, and examples of applications to the general-linear model (regression) and the general linear structural econometric model (simultaneous equations)."--BOOK JACKET.
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arbitrary associated characteristic vector characteristic roots coefﬁcients cofactors column vector complex number conclude Consequently context convention corresponding covariance matrix deﬁned denoted determinant diagonal elements diagonal matrix dimension discussion distribution econometrics elements are zero evident example exists exogenous variables ﬁnd ﬁnite ﬁrst follows function g-inverse given GLSEM Hence Hermite form idempotent identiﬁcation implies inverse ith row Kronecker product least squares linear linearly independent lower triangular m-element column m-element vector matrix of order Moreover multiplication nonnull nonsingular matrix nonzero notation null space obtain OLS estimator operation orthogonal matrix orthonormal parameters permutation matrix polynomial positive deﬁnite positive semideﬁnite properties pseudoinverses q.e.d. Corollary q.e.d. Proposition q.e.d. Remark random variable rank representation respectively result satisﬁes scalar shows square matrix suppose symmetric matrix Toeplitz matrix tr(A triangular matrix unique unity VDECC vec(A vec(X vector space write
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Collecting Spatial Data: Optimum Design of Experiments for Random Fields
Werner G. Müller
No preview available - 2007