An Introduction to Multivariate Statistical Analysis

By W. G. Madow, T. Anderson. 1959

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “MDA whenever P;Qhave different means, and further, it is known to be the “uniformly most powerful” test when P;Qare univariate Gaussians under fairly general assumptions [Kariya, 1981, Simaika, 1941, Anderson, 1958, Salaevskii, 1971]. In a seminal paper by Bai and Saranadasa [1996], the authors prov”
On Brownian Distance Covariance and High Dimensional Data (2009, neutral): “See, for example, Blomqvist [3] , Blum, Kiefer, and Rosenblatt [4] , or methods outlined in Hollander and Wolfe [16] and Anderson [1] .”
Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors (2002, methodology): “We follow Anderson (1984), Tong (1990), and others in working with a particular class of multivariate distributions having t marginals for which the joint distribution is characterized by a symmetric, positive definite matrix R, along with the degrees of freedom.”
Principal Component Analysis of High-Frequency Data (2016, background): “Corollary 1 is the analogue in our context to the classical results on asymptotic theory for PCA by Anderson (1963), who showed that √ n(λ̂− λ) d → N ( 0, 2Diag ( λ(2)1, λ 2 2, .”
Sharp thresholds for high-dimensional and noisy recovery of sparsity (2006, methodology): “ of Lemma 6 Since the matrix XT S XS is Wishart with n degrees of freedom, using properties of the inverse Wishart distribution, we have E[(XT S XS) −1] = (Σ SS) −1 n−s−1 (see Lemma 7.7.1 of Anderson [1]). Thus, we compute E[Y i] = −λn n n−s−1 eT (Σ SS) −1~b, and E[Y′ i ] = σ2 n n n−s−1 eT i (ΣSS) −”
Estimation of parameters and eigenmodes of multivariate autoregressive models (2001, unknown): “Because the determinant of the right-hand side of this formula can be brought into the form [Anderson 1984, Theorem A.3.2] det͑⌬ p ϩ R p T R p ͒ ϭ det ⌬ p ⅐ det͑I ϩ R p ⌬ p Ϫ1 R p T ͒, the downdating formula for the determinant term l p ϭ log det ⌬ p becomes l pϪ1 ϭ l p ϩ log det ͑I ϩ R p ⌬ p Ϫ1 R…”
A MANOVA STATISTIC IS JUST AS POWERFUL AS DISTANCE-BASED STATISTICS, FOR MULTIVARIATE ABUNDANCES (2004, methodology): “This statistic is referred to here as ‘‘LR-IND’’ for easy reference, and is of particular interest because it is a special case of a common MANOVA statistic, Wilk’s L (Anderson 1984:293).”
Conceptual understanding versus algorithmic problem solving: Further evidence from a national chemistry examination (2005, background): “This can lead to a reduction in the number of variables and to the detection of structure in the relationships between variables (Anderson, 1984; Stamovlasis et al., 2004).”