Estimation of Multivariate Means with Heteroscedastic Errors Using Envelope Models

Su, Z. and Cook, R. D.

Statistica Sinica (2013), Vol 23, 213-230.

In this paper, 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 et al. (2010) as a parsimonious version of multivariate linear regression, which achieve efficient estimation of the coefficients by linking the mean function and the covariance structure. In the original development, constant covariance structure is assumed. The heteroscedastic envelope models we proposed are more flexible in allowing a more general covariance structure. Their asymptotic variances and Fisher consistency are studied. Simulations and data example showed 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.

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