An Introduction to Multivariate Statistical Analysis (3rd ed.) (Book)

By C. Anderson‐Cook. 2004

391 citations recorded by the source corpus.

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Citations in the corpus

Sparse PCA: Optimal rates and adaptive estimation (2012, background): “In the conventional setting where the dimension of the data is relatively small compared with the sample size, the principal eigenvectors of the covariance matrix is typically estimated by the leading eigenvectors of the sample covariance matrix which are consistent when the dimension p is fixed, an”
The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data (2007, methodology): “, [22] and [23], we give here a short derivation of some of the most important results including a regression analysis type interpretation and some regularization aspects.”
Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices (2012, background): “For the problem we are concerned with, Anderson [2], Chapter 13, summarized the classical results under the conventional asymptotic regime: p holds fixed and n tends to infinity.”
Statistical Learning with Sparsity: The Lasso and Generalizations (2015, background): “Detailed discussion of graphical models can be found in Whittaker (1990), Lauritzen (1996), Cox and Wermuth (1996), Edwards (2000), Pearl (2000), Anderson (2003), and Koller and Friedman (2009). The Hammersley–Clifford theorem was first announced in the unpublished note of Hammersley and Clifford (1”
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions (2011, background): “In particular, if the let the observation matrix Y ∈ Rd×d be the sample covariance matrix 1 n ∑n i=1 ZiZ i , then some algebra shows that Y = + + W , where = LL is of rank r , and the random matrix W is re-centered Wishart noise [2]—in particular, the zero-mean matrix”
Operator norm consistent estimation of large-dimensional sparse covariance matrices (2008, methodology): “A standard result in Gaussian multivariate analysis (see [2], Theorem 3.”
Spectrum estimation for large dimensional covariance matrices using random matrix theory (2006, background): “(For more details on Anderson’s theorem, we refer the reader to [3], Theorem 13.”
Moments of minors of Wishart matrices (2006, methodology): “We begin by reviewing the well-known formula for a principal minor [2], Section 7.”
Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond (2009, methodology): “7 in [2], we see that, if we denote by τi the decreasingly ordered eigenvalues of T ,”
On Brownian Distance Covariance and High Dimensional Data (2009, unknown): “See, for example, Blomqvist [3], Blum, Kiefer, and Rosenblatt [4], or methods outlined in Hollander and Wolfe [16] and Anderson [1].”
Testing independence in high dimensions with sums of rank correlations (2015, background): “If X is normal, then under the traditional asymptotic setup in which n goes to ∞ while m is fixed, the likelihood ratio test (LRT) statistic converges to a chi-square distribution when H0 is true Anderson (2003).”
A rate of convergence result for the largest eigenvalue of complex white Wishart matrices (2004, unknown): “, [1], Chapters 11 and 13 and, in particular, Theorem 13.”
Optimal hypothesis testing for high dimensional covariance matrices (2012, methodology): “…the literature can be categorized as the following according to the asymptotic regime under which they are suitable: • p ﬁxed and n → ∞ . likelihood In this classical asymptotic regime, conventional tests for (1) include the ratio test (LRT) [1], Roy’s largest root test [16], and Nagao’s test [14].”
Sequences of regressions and their independences (2011, methodology): “There is also a recursive relation for covariances; see Anderson (1958).”
The Variance-Gamma Distribution: A Review (2023, unknown): “That the off diagonal entries are VG distributed can be deduced from the Bartlett decomposition of the Wishart distribution (see Anderson [4]) and the representation (2.18) of the VG distribution in terms of independent normal and chi-square random variables.”
Covariance Estimation: The GLM and Regularization Perspectives (2011, background): “…vector Y = (y1, . . . , yp) ′ with as many as p(p+1)2 constrained parameters plays a central role in virtually all of classical multivariate statistics (Anderson, 2003), time series analysis (Box, Jenkins and Reinsel, 1994), spatial data analysis (Cressie, 1993), variance components and…”
Multispectral classification of grass weeds and wheat (Triticum durum) using linear and nonparametric functional discriminant analysis and neural networks (2008, methodology): “A classic discriminant analysis (Anderson, 2003), nonparametric functional discriminant analysis (Ferraty & Vieu, 2006) and neural networks (Bishop, 1995) were applied to construct a classification rule to discriminate between crop, grass weed species or group of weeds, and soil, based on a sample…”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE I. OPTIMAL RANK-BASED TESTS FOR SPHERICITY (2006, unknown): “see, for example, [1], page 54, [38] or [50].”