Titlebook: Statistics on Special Manifolds; Yasuko Chikuse Book 2003 Springer Science+Business Media New York 2003 correlation.manifold.mathematical

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书目名称Statistics on Special Manifolds读者反馈学科排名

孤僻

Large Sample Asymptotic Theorems in Connection with Tests for Uniformity,ch are sufficient statistics, for the matrix Langevin distributions .(.) and . (.) on the manifolds . and ., respectively. In this chapter, we are concerned with large sample asymptotic theory in connection with parameter estimation and . of distributions against the matrix Langevin distributions on

Evacuate

Asymptotic Theorems for Concentrated Matrix Langevin Distributions,evin distributions .(.) and . (.), with large Λ, on the manifolds . and P., respectively. Here we have the singular value decomposition F = ΓΛΘ′ of rank . (. ≤ .), where . Θ ∈ ., and Λ = diag(λ., ... , λ.), λ. ≥ · · · ≥ λ. > 0, and the spectral decomposition . = ΓΛΓ′ of rank . ≨ ., where . and Λ = d

胡言乱语

armistice

Procrustes Analysis on the Special Manifolds,seful procedures where we transform a set of given matrices to maximum agreement in the least squares sense, for example, by orthogonal matrices [e.g., Ten Berge (1977)], by symmetric matrices [e.g., Higham (1988)], and by such similarity transformation matrices as are used in shape analysis [e.g.,

LAY

Density Estimation on the Special Manifolds, (1956) [see Whittle (1958), Parzen (1962), and Watson and Leadbetter (1963)] and the method of orthogonal series introduced by Čencov (1962) [see Schwartz (1967), Watson (1969), Walter (1977), and Wahba (1981)]; also see Wahba (1975). The methods were extended to vector-variate density estimation b

outset

0930-0325 he space of k­ frames in the m-dimensional real Euclidean space Rm, represented by the set of m x k matrices X such that X‘ X = I , where Ik is the k x k identity matrix, k and the Grassmann manifold Gk,m-k is the space of k-planes (k-dimensional hyperplanes) in Rm. We see that the manifold Pk,m-k o

deviate

Asymptotic Theorems for Concentrated Matrix Langevin Distributions,. We have already seen (see Section 2.3.1) that λ., ... , λ. (> 0) are concentration parameters for the .(., .; .) distribution; note that λ., ... , λ. may also control the concentration of the . (., .; .) distribution when all the λ.s are non-negative.

RADE

foreign

Book 2003f k­ frames in the m-dimensional real Euclidean space Rm, represented by the set of m x k matrices X such that X‘ X = I , where Ik is the k x k identity matrix, k and the Grassmann manifold Gk,m-k is the space of k-planes (k-dimensional hyperplanes) in Rm. We see that the manifold Pk,m-k of m x m or