Multivariate Reduced-Rank Regression: Theory and Applications

By G. Reinsel, R. Velu. 1998

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Implicit Regularization of Discrete Gradient Dynamics in Deep Linear Neural Networks (2019, background): “(4) These problems have explicit solutions depending onX and Y [Reinsel and Velu, 1998, Thm. 2.2].”
Envelopes and reduced-rank regression (2015, methodology): “…of the two methods25 when appropriate and that has the potential to perform better than either of them.26 Reduced-rank regression (Anderson 1951; Izenman 1975; Reinsel and Velu 1998) arises27 frequently in multivariate statistical analysis, and has been applied widely across the applied28 sciences.”
Joint variable and rank selection for parsimonious estimation of high-dimensional matrices (2011, methodology): “They have become a standard tool in time series [Brillinger (1981)], econometrics [Reinsel and Velu (1998)] and machine learning [Izenman (2008)], to name just a few areas.”
Sparse Multivariate Regression With Covariance Estimation (2010, methodology): “A dimensionality reduction approach called reduced-rank regression (Anderson 1951; Izenman 1975; Reinsel and Velu 1998) minimizes (1.1) subject to rank(B) = r for some r ≤ min(p, q).”
Forecasting performance of multivariate time series models with full and reduced rank: An empirical examination (2004, methodology): “Employing a likelihood ratio test (e.g., Kohn, 1979; Reinsel & Velu, 1998, p. 118), we also find that the rank of the coefficient matrix is four (with a p-value of 0.630).”
Dimension reduction and coefficient estimation in multivariate linear regression (2007, methodology): “The first order optimality condition for (24) yields nλ = X̃ ′ iỸi − X̃ ′ iX̃id̂i, (25)”
Optimal selection of reduced rank estimators of high-dimensional matrices (2010, methodology): “The following computationally eﬃcient procedure for calculating each (cid:98) B k has been suggested by Reinsel and Velu (1998).”
Theoretical Analysis of Bayesian Matrix Factorization (2011, methodology): “With appropriate pre-whitening (Hyvärinen et al., 2001), reduced rank regression (Baldi and Hornik, 1995; Reinsel and Velu, 1998), canonical correlation analysis (Hotelling, 1936; Anderson, 1984), partial least-squares (Wold, 1966; Worsley et al., 1997; Rosipal and Krämer, 2006), and multi-task…”
Nonlinearity and Flight‐to‐Safety in the Risk‐Return Trade‐Off for Stocks and Bonds (2019, unknown): “…hypotheses of interest: H1,0 : bjh φh = 0 H1,A : b j h φh 6= 0 H2,0 : bhφh = 0n H2,A : bhφh 6= 0n H3,0 : φh (v̄) = 0 H3,A : φh (v̄) 6= 0 (3.13) The first hypothesis tests the null that φh does not predict excess returns Rxjt+h of asset 3See Reinsel and Velu (1998) for a general introduction.”
Reduced rank stochastic regression with a sparse singular value decomposition (2012, methodology): “This type of model formation was first suggested in the seminal work of Anderson (1951) and was studied by Reinsel and Velu (1998), chapter 3, under the classical least squares setting.”
Global analytic solution of fully-observed variational Bayesian matrix factorization (2013, methodology): “Finally, we applied VBMF to a reduced rank regression (RRR) (Reinsel and Velu, 1998) task, and show the results in Figure 7.”
ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION (2010, background): “Notable among them is the class of reduced-rank regressions, which allow for the possibility that rank(β) min(p, r) (Reinsel and Velu (1998)).”