Inner Envelopes: Efficient Estimation in Multivariate Linear Regression

Su, Z. and Cook, R. D.

Biometrika (2012), Vol 99, 687-702.

In this article we propose a new model, called the inner envelope model, which leads to efficient estimation in the context of multivariate normal linear regression. The asymptotic distribution and the consistency of its maximum likelihood estimators are established. Theoretical results, simulation studies and examples all show that the efficiency gains can be substantial relative to standard methods and to the maximum likelihood estimators from the envelope model introduced recently by Cook et al. (2010). Compared to the envelope model, the inner envelope model is based on a different construction and it can produce substantial efficiency gains in situations where the envelope model offers no gains. In effect, inner envelopes open a new frontier on the way in which reducing subspaces can be used to improve efficiency in multivariate problems.

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