Principal Components, Sufficient Dimension Reduction, and Envelopes

2018 ◽  
Vol 5 (1) ◽  
pp. 533-559 ◽  
Author(s):  
R. Dennis Cook
Keyword(s):  
Dimension Reduction ◽  
Principal Components ◽  
Sufficient Dimension Reduction

scholarly journals Sufficient dimension reduction and prediction in regression

2009 ◽  
Vol 367 (1906) ◽  
pp. 4385-4405 ◽  
Author(s):  
Kofi P. Adragni ◽  
R. Dennis Cook
Keyword(s):  
Applied Sciences ◽  
Dimension Reduction ◽  
Principal Components ◽  
Sufficient Dimension Reduction ◽  
The Past ◽  
New Methods ◽  
Technological Advances ◽  
Broad Overview

Dimension reduction for regression is a prominent issue today because technological advances now allow scientists to routinely formulate regressions in which the number of predictors is considerably larger than in the past. While several methods have been proposed to deal with such regressions, principal components (PCs) still seem to be the most widely used across the applied sciences. We give a broad overview of ideas underlying a particular class of methods for dimension reduction that includes PCs, along with an introduction to the corresponding methodology. New methods are proposed for prediction in regressions with many predictors.

scholarly journals Cumulative Median Estimation for Sufficient Dimension Reduction

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 138-145
Author(s):  
Stephen Babos ◽  
Andreas Artemiou
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Sufficient Dimension Reduction

In this paper, we present the Cumulative Median Estimation (CUMed) algorithm for robust sufficient dimension reduction. Compared with non-robust competitors, this algorithm performs better when there are outliers present in the data and comparably when outliers are not present. This is demonstrated in simulated and real data experiments.

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