Partial Envelopes for Efficient Estimation in Multivariate Linear Regression

Su, Z. and Cook, R. D.

Biometrika (2011), Vol. 98, 133-146.

We introduce the partial envelope model, which leads to a parsimonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve massive efficiency gains compared with the standard model in the estimation of the coefficients for the selected predictors. The partial envelope model is a variation in the envelope model proposed by Cook et al. (in Envelope models for parsimonious and efficient multivariate linear regression. Statist. Sinica 20, 927–1010.) but, as it focuses on part of the predictors, it has looser restrictions and can further improve the efficiency. We develop maximum likelihood estimation for the partial envelope model and discuss applications of the bootstrap. An example is provided to illustrate some of its operating characteristics.


MATLAB toolbox envlp
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