Abstract:
| We propose a scaled envelope model, which is a scale invariant envelope model that can achieve efficient estimation in multivariate linear regression. Compared to the envelope model introduced by Cook et al. (2010), the scaled envelope model is invariant under scale transformations of the responses. The algebraic mechanism underlying the scaled envelope model is connected with similarity transformations. Theoretical results, numerical experiments and an example all show that by considering scaling, we can expand the effective scope of envelope constructions and achieve efficiency gains compared to the standard model and to the envelope model.
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