Envelopes and Partial Least Squares Regression

Cook, R. D., Helland, I. S. and Su, Z.

Journal of the Royal Statistical Society: Series B (2013) Vol 75, 851-877.

We build connections between envelopes, a recently proposed context for efficient estimation in multivariate statistics, and multivariate partial least squares (PLS) regression. In particular, we establish an envelope as the nucleus of both univariate and multivariate PLS, which opens the door to pursuing the same goals as PLS but using different envelope estimators. It is argued that a likelihood-based envelope estimator is less sensitive to the number of PLS components selected and that it outperforms PLS in prediction and estimation.

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