Slope estimation in structural line-segment heteroscedastic measurement error models

This paper extends the line-segment parametrization of the structural measurement error 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 which validate our results and demonstrate that our estimates are more precise than estimates under a different model when the measurement error variance is not small. Lastly, we illustrate our estimation approach using real data involving heteroscedastic measurement error, and compare its performance to that of earlier models.