标题： 加权包络估计以处理模型选择中的变异性 显示英文标题

标题： Weighted envelope estimation to handle variability in model selection

摘要： 包络方法可以在多元统计问题中提供显著的效率提升，但在某些应用中，包络维度的估计可能会引起选择波动性，从而削弱这些收益。 目前的包络方法并未考虑由此选择可能产生的附加方差。 本文通过开发加权包络估计量来规避维度选择的波动性。 我们估计量的理论依据得到证明，并且残差自助法用于估计其渐近方差的有效性也得以确立。 模拟研究和对真实数据集的分析展示了我们加权包络估计量的实用性。 显示英文摘要

摘要： 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.