A Note on Adapting for Heteroscedasticity When the Variances Depend on the Mean.
Abstract
This document considers the normal-theory regression model when the error disturbances are heteroscedastic, i.e., have non-constant variances. The author distinguishes two cases: 1)predictor heteroscedasticity, where the variances depend on a function g of known quantities and 2) mean heteroscedasticity, where the variances depend on a function g of the means. For the case where g is unknown, Carroll showed by construction that, in certain cases, it is possible to estimate the regression parameter asymptotically as well as if g were known and weighted least squares applied. This document reconsiders this problem from the information bound theory of Begun, Hall, Huang & Wellner. For mean heteroscedasticity, a rather surprising result is obtained. If g were known in this case, Jobson & Fuller showed that the maximum likelihood estimate is asymptotically more efficient than weighted least squares with known weights. When g is unknown the full Jobson & Fuller improvements are not possible; however, we show that one can, in theory, attain asymptotically better performance than weighted least squares with known weights. Keywords: Adaptation; Linear models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1985
- Accession Number
- ADA168481
Entities
People
- David Ruppert
- Leonard A. Stefanski
- Raymond J. Carroll
Organizations
- University of North Carolina at Chapel Hill