Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.
Bibliographical notePublisher Copyright:
© 2017 Biometrika Trust.
Copyright 2017 Elsevier B.V., All rights reserved.
- Dimension reduction
- Envelope model
- Model selection
- Residual bootstrap
- Variance reduction