2014/03/17 by R. Dennis Cook, Xin Zhang, Cook, R. Dennis +1 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1403.4138
openalex publication_date 2014/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.