Multivariate Statistics: A Vector Space ApproachBuilding from his lecture notes, Eaton (mathematics, U. of Minnesota) has designed this text to support either a one-year class in graduate-level multivariate courses or independent study. He presents a version of multivariate statistical theory in which vector space and invariance methods replace to a large extent more traditional multivariate methods. Using extensive examples and exercises Eaton describes vector space theory, random vectors, the normal distribution on a vector space, linear statistical models, matrix factorization and Jacobians, topological groups and invariant measures, first applications of invariance, the Wishart distribution, inferences for means in multivariate linear models and canonical correlation coefficients. Eaton also provides comments on selected exercises and a bibliography. |
Contents
RANDOM VECTORS | 70 |
THE NORMAL DISTRIBUTION ON A VECTOR SPACE | 103 |
LINEAR STATISTICAL MODELS | 132 |
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A₁ a₁₁ assume Ax₁ B₁ B₂ C₁ canonical correlation chapter compact consider continuous homomorphism coordinate Cov(X covariance defined denote density diagonal elements eigenvalues equivariant Example follows G-invariant G₁ G₂ Gauss-Markov estimator given group G H₁ implies independent inner product space invariant function invariant integrals invariant measure Lebesgue measure left invariant likelihood ratio test linear model linear transformation M₁ MANOVA matrix maximal invariant maximum likelihood estimator mean vector multivariate n₁ nonsingular normal distribution notation numbers one-to-one orthogonal projection orthonormal basis p₁ parameter positive definite probability measure Proof Proposition random variables random vector rank relatively invariant result S₁ satisfies self-adjoint statistic subspace Suppose testing problem Theorem tion U₁ unique V₁ V₂ vector space verify w₁ W₂ Wishart distribution X₁ X₂ y₁ Z₁ zero λ₁ μ₁ σ²