Abstract
Envelopes were recently proposed by Cook, Li and Chiaromonte as a method for reducing estimative and predictive variations in multivariate linear regression. We extend their formulation, proposing a general definition of an envelope and a general framework for adapting envelope methods to any estimation procedure. We apply the new envelope methods to weighted least squares, generalized linear models and Cox regression. Simulations and illustrative data analysis show the potential for envelope methods to significantly improve standard methods in linear discriminant analysis, logistic regression and Poisson regression. Supplementary materials for this article are available online.
Original language | English (US) |
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Pages (from-to) | 599-611 |
Number of pages | 13 |
Journal | Journal of the American Statistical Association |
Volume | 110 |
Issue number | 510 |
DOIs | |
State | Published - Apr 3 2015 |
Bibliographical note
Publisher Copyright:© 2015 American Statistical Association.
Keywords
- Generalized linear models
- Grassmannians
- Weighted least squares