Algorithms for Envelope Estimation. Issue 1 (2nd January 2016) - Cook, R. Dennis; Zhang, Xin
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 n -consistency of the algorithm. Supplementary materials for this article are available online.