Comparing Different Estimators in a Nonlinear Measurement Error Model

Kukush, Alexander; Schneeweiß, Hans; Wolf, R. (2002): Comparing Different Estimators in a Nonlinear Measurement Error Model. Collaborative Research Center 386, Discussion Paper 244

Abstract

A nonlinear structural errors-in-variables model is investigated, where the response variable has a density belonging to an exponential family and the error-prone covariate follows a Gaussian distribution. Assuming the error variance to be known, we consider two consistent estimators in addition to the naive estimator. We compare their relative efficiencies by means of their asymptotic covariance matrices for small error variances. The structural quasi score (SQS) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. Consistency and asymptotic normality of this estimator is proved. The corrected score (CS) estimator is based on an error-corrected likelihood score function. For small error variances the SQS and CS estimators are approximately equally efficient. The polynomial model and the Poisson regression model are explored in greater detail.

• Item Type: Paper (Research Paper)
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English