Amemiya's form of the weighted least squares estimator

Roger Koenker, José A. F. Machado, Christopher L. Skeels, A. H. Welsh

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Amemiya's estimator is a weighted least squares estimator of the regression coefficients in a linear model with heteroscedastic errors. It is attractive because the heteroscedasticity is not parametrized and the weights (which depend on the error covariance matrix) are estimated nonparametrically. This paper derives an asymptotic expansion for Amemiya's form of the weighted least squares estimator, and uses it to discuss the effects of estimating the weights, of the number of iterations, and of the choice of the initial estimate. The paper also discusses the special case of normally distributed errors and clarifies the particular consequences of assuming normality.

Original languageEnglish
Pages (from-to)155-174
Number of pages20
JournalAustralian Journal of Statistics
Issue number2
Publication statusPublished - 1 Jan 1993


  • heteroscedasticity
  • robustness
  • Weighted least squares


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