Conditional likelihood inference in a heteroscedastic functional measurement error model

Abstract

In this paper, we deal with inference about the structural parameters in a heteroscedastic functional measurement error models under the normal distribution assumption. Given a minimal sufficient statistic for the incidental parameters, the conditional maximum likelihood (CML) approach is used. We show that CML estimators have explicit expressions and their sampling distribution is exact. We also show that the classical test statistics to test hypotheses of interest coincide and have exact distributions. We apply the statistical inference tools developed to a data set on comparison of measurement methods.