Matrix Algebra Useful for Statistics

By Abel Rodrigues. 2007

325 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9ef23982b11fc3af7a069c66cf0e692560390dc6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories (2009, background): “An extension to the multivariate case with p attributes of interest is straightforward as it raises no new issues except for a necessary switch to matrix algebra (Searle, 1982).”
Ones Assignment Method for Solving Assignment Problems (2012, background): “One of the operations associated with matrices is calculation of scalar value known as the determinant of a square matrix [6].”
Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression (2014, unknown): “By equation (33) of page 355 in [26], ∣∣E0(σ̂ 2 n )− σ 2 0 ∣∣ = ∣∣n−1σ 2 0 tr(U) − σ 2 0 ∣∣+ n−1(F0 − Bη) U(F0 − Bη) n−1 [ tr(In − U) + (F0 − Bθ∞) U(F0 − Bθ∞) (7.”
A new autocovariance least-squares method for estimating noise covariances (2006, unknown): “C ¯ A N−2 · · · C 0    Ψ = Γ   N j=1 (−AL)   TWMCC Technical Report 2003-04 5 In this result and those to follow, we employ the standard definitions of the Kronecker product, Kronecker sum and the direct sum [6] [20].”
Generalized linear array models with applications to multidimensional smoothing (2006, unknown): “We use a well known identity of the Kronecker product (Searle, 1982, p333) to write the linear predictor as where £ , c 1 £ c 2 , is the coe–cient matrix corresponding to (cid:181) , i.e., vec ( £ ) = (cid:181) .”
Resonance to archetypes in media: There’s some accounting for taste (2009, background): “the determinant could not be calculated, and the matrix was singular (Searle, 1982).”
Nonlinear Compensation Using the Gauss–Newton Method for Noise-Robust Speech Recognition (2012, methodology): “For the derivative of the main probability term, we make use of the identity [54]”
Advanced Multivariate Statistics with Matrices (2005, background): “Sometimes the relation in the next theorem is called Aitken’s integral (Searle, 1982).”