Matrix Analysis for Statistics

By Andreas Karlsson. Technometrics, 2007

383 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/10e7658a087514ca908c2686e5127d11c3f90fc5

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Weed Abundance, Distribution, Diversity, and Community Analyses (2015, neutral): “N Next, randomly select n distinctly different numbers, either by means of a table of random numbers (Snedecor and Cochran 1967) or by means of a computer program that produces such a table.”
A continuous time Markov model for the length of stay of elderly people in institutional long‐term care (2005, background): “The matrix exponential is defined in the usual manner; see for example Schott (1997) .”
A Swiss Army Infinitesimal Jackknife (2018, methodology): “We will use Schott [2016, Theorem 5.20] and the associated discussion, which states the following general result.”
On Randic Energy of Graphs (2014, background): “[13] Let B be a p × p symmetric matrix and let Bk be its leading k × k submatrix.”
Reduced rank stochastic regression with a sparse singular value decomposition (2012, methodology): “The symbol ‘⊗’ denotes the Kronecker product and we shall freely make use of several properties of the Kronecker product; see Schott (2005), chapter 8.”
Maximum‐likelihood estimation for multivariate spatial linear coregionalization models (2007, background): “From the well-known property of matrix derivative (see, e.g., Schott, 1997, p333), we have À @ log V k j j @y ij;k ¼ @ log V À1 k @y ij;k ¼ tr V k @V À1 k @y ij;k ¼ d ij s ij;k where d ij is 2 if i 6 ¼ j and 1 otherwise.”
Advanced Multivariate Statistics with Matrices (2005, background): “Matrix theory, which is a cornerstone of multivariate analysis starting from T. W. Anderson, has been enriched during the last few years by several new volumes: Bhatia (1997), Harville (1997), Schott (1997b), Rao & Rao (1998), Zhang (1999).”
Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis (2010, neutral): “By the chain rule and standard matrix calculus results (e.g., Schott, 1997), one can find that qlð jZÞ q 0 ¼ qlð jZÞ q 0r q 0 r q 0 ¼ qlð jZÞ q 0r L; and q2lð jZÞ q q 0 ¼ q q qlð jZÞ q 0 ¼ L0 q 2lð jZÞ q rq 0 r L: This implies that one can first take the complete data derivatives with respect to r,…”
Marginal tests with sliced average variance estimation (2007, background): “When X is normal, we have H TZ ∼ N(0, Ip−m), and var(H TZ ⊗ H TZ)/2 is a projection matrix with rank (p − m)(p − m + 1)/2 (Schott, 1997, Theorem 7·10), so all its nonzero eigenvalues are equal to 1.”
A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. (2006, background): “Let ε max i i(M ε211 ) , then clearly (ε) 0, and because M ε211 is positive, by Theorem 7.44 of Schott (1997) [1], as indicated above, the corresponding eigenvector x(ε) satisfies M ε211 )abs[x(ε)] M(ε)abs[x(ε)].”
On Randić energy (2014, background): “[18] Let B be a p × p symmetric matrix and let Bk be its leading k × k submatrix.”
Nonparametric methods for unbalanced multivariate data and many factor levels (2008, background): “uniqueness and existence, this inverse also defines a contin uous mapping (see Schott [ 16 ], Chapter 5).”