Weighted envelope estimation to handle variability in model selection

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 validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and an analysis on a real data set illustrate the utility of our weighted envelope estimator.