ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION

By R. Dennis Cook, Bing Li, Francesca Chiaromonte. 2010

198 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/436c91247241e9c486e79b796231ff39dc64e49b

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Citations in the corpus

Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression (2016, unknown): “The envelope model (Cook et al., 2010) makes use of the stochastic relationships among the elements of Y , and identifies a part of the response that is immaterial to changes in X .”
Envelopes and reduced-rank regression (2015, methodology): “…maximum likelihood estimators.269 We focus attention on the comparison between β̂RE and β̂RR because (1) comparisons between270 β̂Env and β̂OLS can be found in Cook et al. (2010); and (2) the advantage of β̂RE over β̂Env is271 similar to the advantage of β̂RR over β̂OLS, which is due to the…”
Partial least squares prediction in high-dimensional regression (2019, methodology): “Cook, Helland and Su [12] established a population connection between PLS regression and envelopes [14] in the context of multivariate linear regression, provided the first firm PLS model and showed that envelope estimation leads to root-n consistent estimators whose performance dominates that of PL”
Inner envelopes: Efficient estimation in multivariate linear regression (2012, background): “As β = 1ηT1 + 0 BηT2, we follow Lemma 4.2 in Cook et al. (2010) and write L = L1L2, where L1 = {det( 1)}−n/2 × etr{−2−1(U 1 − Fη1) −11 (U 1 − Fη1)T}, L2 = {det( 0)}−n/2 × etr{−2−1(U 0 − Fη2 BT) −10 (U 0 − Fη2 BT)T}.”
ldr: An R Software Package for Likelihood-Based Su?cient Dimension Reduction (2014, methodology): “…the predictor vector X given the response Y , and include covariance reduction (CORE, Cook and Forzani 2008a), likelihood acquired directions (LAD, Cook and Forzani 2009), principal ﬁtted components (PFC, Cook 2007; Cook and Forzani 2008b), and the envelope model (Cook, Li, and Chiaromonte 2010).”