Slope estimation in structural line-segment heteroscedastic measurement error models

This paper extends the line-segment parametrization of the structural measurement error (ME) model to situations in which the error variance on both variables is not constant over all observations. Under these conditions, we develop a method-of-moments estimate of the slope, and derive its asymptotic variance. We further derive an accurate estimator of the variability of the slope estimate based on sample data in a rather general setting. We perform simulations that validate our results and demonstrate that our estimates are more precise than estimates under a different model when the ME variance is not small. Finally, we illustrate our estimation approach using real data involving heteroscedastic ME, and compare its performance with that of earlier models.