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Journal Article

# Sampling Experiments on the Estimation of Parameters in Heteroscedastic Linear Regression

John A. Jacquez and Marija Norusis
Biometrics
Vol. 29, No. 4 (Dec., 1973), pp. 771-780
DOI: 10.2307/2529142
Stable URL: http://www.jstor.org/stable/2529142
Page Count: 10

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## Abstract

Sampling experiments were conducted to compare least squares (LS) and weighted least squares (WLS) estimators in heteroscedastic linear regression. Variance estimates obtained both from replicates, s$_i^2$, and from a modification of $Rao's [1970] MINQUE estimator, \tilde{s}_i^2,$ were used as weighting factors in WLS estimation. Efficiency comparisons of the $LS, WLS(s_i^2), and WLS(\tilde{s}_i^2) estimators$ were based on the generalized variance, the Euclidean norm, the variance of the slope estimator, and the variance of the estimator of E(y $\mid$ x). It was found that LS estimators are remarkably robust, and only for marked variance heterogeneity or many replicates at each point are weighted estimators uniformly better. In general, unless the number of replicates at each point is large ($\geq$10), $WLS(\tilde{s}_i^2) estimators are more efficient than WLS(s_i^2).$

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