TY - JOUR

T1 - Amemiya's form of the weighted least squares estimator

AU - Koenker, Roger

AU - Machado, José A. F.

AU - Skeels, Christopher L.

AU - Welsh, A. H.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

KW - heteroscedasticity

KW - robustness

KW - Weighted least squares

UR - http://www.scopus.com/inward/record.url?scp=84990495169&partnerID=8YFLogxK

U2 - 10.1111/j.1467-842X.1993.tb01322.x

DO - 10.1111/j.1467-842X.1993.tb01322.x

M3 - Article

AN - SCOPUS:84990495169

VL - 35

SP - 155

EP - 174

JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

SN - 0004-9581

IS - 2

ER -