Weighted envelope estimation to handle variability in model selection

TL;DR

This paper introduces a weighted envelope estimator to reduce variability caused by model selection in envelope methodology, improving efficiency in multivariate analysis.

Contribution

The paper develops a novel weighted envelope estimator that accounts for selection volatility, with theoretical validation and practical demonstration.

Findings

The weighted estimator reduces variance due to model selection.

Bootstrap methods accurately estimate the estimator's variance.

Simulation and real data show improved efficiency.

Abstract

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.