Envelopes and partial least squares regression

By R. Dennis Cook, Inge S. Helland, Zhihua Su. 2013

152 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Food Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9f9efa42188e0a0d76767c76ea95f99afd7893af

How researchers see this paper

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

In Analytical Chemistry

1. Liliana Forzani
2. Xin Zhang
3. R. Dennis Cook
4. S. Pal
5. Kshitij Khare
6. Zhihua Su
7. Shanshan Ding

In Food Science

1. Liliana Forzani
2. Xin Zhang
3. R. Dennis Cook
4. S. Pal
5. Kshitij Khare
6. Zhihua Su

In Statistics and Probability

1. R. Dennis Cook
2. Xin Zhang
3. Shanshan Ding
4. Liliana Forzani
5. Zhihua Su
6. Kshitij Khare
7. S. Pal
8. Xiangrong Yin

Citations in the corpus

• Matrix variate regressions and envelope models (2016, background): “ariation var( Q E Y )is substantially larger than the material variation var( P E Y |X ). Recent developments of envelopes under other settings may be found in, for example, Su and Cook (2011, 2012), Cook et al. (2013), and Cook and Zhang (2015). In particular, Cook and Zhang (2015) studied the rela”
• Partial least squares prediction in high-dimensional regression (2019, methodology): “PLS can be seen as an envelope method as follows [12].”
• A Bayesian approach for envelope models (2017, methodology): “Additionally, an improvement of the likelihood ratio test for the envelope model has been proposed in [14], and a connection between envelope models and partial least squares (PLS) has also been established in [4].”
• Foundations for Envelope Models and Methods (2015, methodology): “Cook, Helland, and Su (2013) used envelopes to study predictor reduction in multivariate linear regression (1.1), where the predictors are stochastic with var(X) = X.”
• Envelopes and reduced-rank regression (2015, unknown): “The rest of the proof621 is similar to the proof of Proposition 4.2 in Cook et al. (2013) that622 log |GTΣG|+ log |GTΣ−1Y G| = log |GTΣG|+ log |GT0 ΣYG0| = log |GTΣG|+ log |GT0 (Σ + βΣXβT )G0| ≥ log |GTΣG|+ log |GT0 ΣG0| ≥ log |Σ|, where the first inequality achieves its lower bound if span(β) ⊆…”
• Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression (2016, unknown): “Moreover, a connection between the envelope model and partial least squares that has allowed for a new understanding of the working mechanism of partial least squares was established by Cook et al. (2013).”