Alternative covariance estimates in a replicated measurement error model with correlated, heteroscedastic errors

Abstract

The article concerns covariance estimates in a replicated measurement error model with correlated, heteroscedastic errors. Freedman has conjectured that using more of the data will improve estimates of covariance matrices and result in a more efficient estimate of the coefficient of the regression model. The paper confirms the conjecture asymptotically for the case that all random variables are normally distributed, but the gain is not substantial.

Keywords:

• Asymptotics
• Covariance estimation
• Heteroscedasticity
• Measurement error
• Relative efficiency