The envelope model was first introduced as a parsimonious version of multivariate linear regression. It uses dimension reduction techniques to remove immaterial variation in the data and has the potential to gain efficiency in estimation and improve prediction. Many advances have taken place since its introduction, and the envelope model has been applied to many contexts in multivariate analysis, including partial least squares, generalised linear models, Bayesian analysis, variable selection and quantile regression, among others. This article serves as a review of the envelope model and its developments for those who are new to the area.
This content will become publicly available on November 28, 2024
Envelopes for multivariate linear regression with linearly constrained coefficients
A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection.
more » « less- Award ID(s):
- 1916013
- NSF-PAR ID:
- 10479342
- Publisher / Repository:
- Wileys
- Date Published:
- Journal Name:
- Scandinavian Journal of Statistics
- ISSN:
- 0303-6898
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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