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Statistica Sinica 23 (2013), 213-230

doi:http://dx.doi.org/10.5705/ss.2010.240





ESTIMATION OF MULTIVARIATE MEANS WITH

HETEROSCEDASTIC ERRORS USING

ENVELOPE MODELS


Zhihua Su and R. Dennis Cook


University of Florida and University of Minnesota


Abstract: In this article, we propose envelope models that accommodate heteroscedastic error structure in the framework of estimating multivariate means for different populations. Envelope models were introduced by Cook, Li, and Chiaromonte (2010) as a parsimonious version of multivariate linear regression that achieves efficient estimation of the coefficients by linking the mean function and the covariance structure. In the original development, constant covariance structure was assumed. The heteroscedastic envelope models we propose are more flexible in allowing a more general covariance structure. Their asymptotic variances and Fisher consistency are studied. Simulations and data examples show that they are more efficient than standard methods of estimating the multivariate means, and also more efficient than the envelope model assuming constant covariance structure.



Key words and phrases: Dimension reduction, envelope model, Grassmann manifold, reducing subspace.

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