Algorithms for envelope estimation
R. Dennis Cook, Xin Zhang
TL;DR
This paper introduces a fast, general 1D algorithm for envelope estimation in multivariate linear regression, leveraging a structural property of envelopes and proving its statistical consistency.
Contribution
It proposes a novel, efficient 1D algorithm for envelope estimation, with theoretical guarantees of Fisher and root-n consistency.
Findings
The algorithm is fast and widely applicable.
It reveals a structural property of envelopes.
Theoretical proofs confirm Fisher and root-n consistency.
Abstract
Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and root-n-consistency of the algorithm.
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Statistical Methods and Inference · Statistical Methods and Bayesian Inference