Foundations for Envelope Models and Methods

By R. Dennis Cook, Xin Zhang. 2015

99 citations recorded by the source corpus.

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.

Subfields: Food Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e46c691e9f00d74694f893fc71b89f709a41bcfd

Citations in the corpus

• Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression (2016, unknown): “Building on the development in Cook et al. (2010), several papers have applied the idea of enveloping to more general contexts, and have proposed new models to achieve even greater gains in efficiency; see, e.g., Su & Cook (2011), Cook & Su (2013), and Cook & Zhang (2015).”