Inference in a structural heteroskedastic calibration model

The main goal of this paper is to study inference in an heteroskedastic calibration model. We embrace a multivariate structural model with known diagonal covariance error matrices, which is a common setup when different measurement methods are compared. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators and a graphical device for model checking are also discussed. Test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. Results of simulations comprising point estimation, interval estimation, and hypothesis testing are reported. An application to a real data set is given. Up to best of our knowledge, topics such as model checking and hypotheses testing have received only scarce attention in the literature on calibration models.