1969
DOI: 10.1080/01621459.1969.10501063
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Variance of Weighted Regression Estimators when Sampling Errors are Independent and Heteroscedastic

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Cited by 30 publications
(16 citation statements)
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“…The effect of estimated variance and covariance parameters on mean squared error of estimation or prediction has been considered previously in the context of time series models (Yamamoto (1976), Reinsel (1980), Fuller andHasza (1981)), random and mixed linear models (Khatri and Shah (1981), Reinsel (1984), Kackar and Harville (1984)), the heteroscedastie regression model (Bement and Williams (1969), Carroll et al (1988)), and the general linear model (Toyooka (1982), Rothenberg (1984), Eaton (1985), Harville (1985), Harville and Jeske (1992)). The present paper follows closely the development of Harville (1985) and Harville and Jeske (1992), and much of it may be viewed as an extension of their results to models with generalized covariances.…”
Section: Introductionmentioning
confidence: 99%
“…The effect of estimated variance and covariance parameters on mean squared error of estimation or prediction has been considered previously in the context of time series models (Yamamoto (1976), Reinsel (1980), Fuller andHasza (1981)), random and mixed linear models (Khatri and Shah (1981), Reinsel (1984), Kackar and Harville (1984)), the heteroscedastie regression model (Bement and Williams (1969), Carroll et al (1988)), and the general linear model (Toyooka (1982), Rothenberg (1984), Eaton (1985), Harville (1985), Harville and Jeske (1992)). The present paper follows closely the development of Harville (1985) and Harville and Jeske (1992), and much of it may be viewed as an extension of their results to models with generalized covariances.…”
Section: Introductionmentioning
confidence: 99%
“…Unweighted regression involves the assumption that the r 2 i are equal, which is unlikely to be true. However, unlike the weighted regression methods, it does not require estimation of r 2 p and does not depend on how well the r 2 i are estimated; Bement & Williams (1969) suggest that at least ten degrees of freedom are required when estimating each r 2 i in a weighted regression.…”
Section: A P P R O a C H E S T O T H E S E C O N D S T A G E O F T H mentioning
confidence: 99%
“…It is difficult to obtain a simple expression for the bias inVb W , owing to the estimation of the weights (Bement & Williams 1969). For unweighted regression, the bias inVb U can be written as (Appendix A)…”
Section: )mentioning
confidence: 99%
“…In [2], the efficiency of the weighted mean with estimate variances was studied. The variance of the weighted regression was derived in [3]. A new estimator that is more efficient than the maximum likelihood estimate was developed in [4].…”
Section: Introductionmentioning
confidence: 99%