A matrix handbook for statisticians

By George A. F. Seber. 2007

563 citations recorded by the source corpus.

Subfields: Materials Chemistry, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/eaaf6dfc42aa9d0e11e5f0989940518f2024c591

How researchers see this paper

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

In Materials Chemistry

1. Ke-Xin Li
2. David Ruppert
3. Xiang-Gen Xia
4. Li You
5. Ni Ma
6. Björn E. Ottersten
7. Daniel J. Lizotte
8. Xiqi Gao

In Safety, Risk, Reliability and Quality

1. Ke-Xin Li
2. David Ruppert
3. Xiang-Gen Xia
4. Li You
5. Ni Ma
6. Björn E. Ottersten
7. Daniel J. Lizotte
8. Xiqi Gao

Citations in the corpus

• Covariance Regression Analysis (2017, unknown): “For instance, the similarity in social network studies (Scott 1988; Wasserman 1994) can be defined as follows: w ( Xj1 ,Xj2 ) = { 1 if two individuals j1 and j2 known each other; 0 otherwise.”
• Massive MIMO Transmission for LEO Satellite Communications (2020, methodology): “From (24), we can obtain that ASLNR max k with the proposed sCSI based precoder can be upper bounded by where (a) follows from that γ i v i v H i is positive semidefinite for ∀ i , and (b) follows from the Sherman-Morrison formula [39, Eq.”
• Fast bivariate P‐splines: the sandwich smoother (2010, methodology): “Applying a well-known identity of the tensor product (Seber 2007, pp. 240) to (1) gives ˆ y = ( S 2 ⊗ S 1 ) y .”
• Improved multivariate portmanteau test (2012, unknown): “ˆ m|≈1. On the other hand, when there is autocorrelation present, |Rˆ m|will be expected to be smaller than 1. To see this we repeatedly apply the formula for the determinant of a partitioned matrix [Seber, 2008, §14.1], |Rˆ m|= Ym ℓ=1 |Ik −Rˆ (ℓ)Rˆ −1 ℓ−1 Rˆ′ ℓ) |, (14) where Rˆ (ℓ) = [ Rˆ 1 : ···:”
• Realized Wishart-Garch: A Score-Driven Multi-Asset Volatility Model (2016, unknown): “Here Lk ¼ ðD0kDkÞ 1D0k is the Moore–Penrose inverse of the duplication matrix Dk. Additional properties and results related to these matrices can be found in Magnus and Neudecker (2007) and Seber (2007).”
• Beam Division Multiple Access Transmission for Massive MIMO Communications (2015, background): “Therefore, there exists a unitary matrix U, satisfying UCBCUH D1/2BD [41].”
• Pilot Reuse for Massive MIMO Transmission over Spatially Correlated Rayleigh Fading Channels (2015, methodology): “By setting the derivative of ǫ u with respect to W ∗ [34] to zero, where (a) follows from A T = A ∗ for the Hermitian matrix A , we can obtain   Substituting (60) into (58), we can obtain the corresponding MSE-SD as   where (a) follows from the Woodbury matrix inversion identity [33, Prop.”
• Convergent Fitted Value Iteration with Linear Function Approximation (2011, background): “It is known [18] that for a linear operator M , ||M ||op(2) is given by the largest singular value of M .”
• Semiparametric Estimation and Testing of Smooth Coefficient Spatial Autoregressive Models (2017, unknown): “By Weyl’s theorem (Seber, 2008, p.117), we have∥∥∥[In − ρ̂ (Z) W]−1∥∥∥ sp = ‖In − ρ (Z) W‖sp +O (‖[ρ̂ (Z)− ρ (Z)] W‖) , where we obtain, under Assumption 5, that ‖[ρ̂ (Z)− ρ (Z)] W‖ = n∑ i=1 ∑ j 6=i [ρ̂ (zi)− ρ (zi)]2 [ρ̂ (zi)− ρ (zj)]2w2ij 1/2 = Op(‖H‖2 + √ lnn n |H| ) .”
• Robust High-Dimensional Precision Matrix Estimation (2014, unknown): “its inverse into Σˆ = Σˆ XX σˆXy σˆ′ Xy σˆyy ! Θˆ = Θˆ XX θˆ Xy θˆ ′ Xy θˆ yy ! the least squares estimator can be rewritten as βˆ LS = Σˆ−1 XXσˆ Xy= − 1 θyy Θˆ using the partitioned inverse formula [Seber, 2008, 14.11]. With the correlation based precision matrix estimate Θˆ S((X,y)) computed joint”