  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.
