Polynomial regression with heteroscedastic measurement errors in both axes: Estimation and hypothesis testing

This article investigates point estimation and hypothesis testing in a polynomial regression model with heteroscedastic measurement errors present in both response and regressor variables. For point estimation, the adjusted least squares method and its modifications are developed. These methods can treat both functional and structural models, and models with or without an equation error. For hypothesis testing, the Wald-type and score-type tests are discussed. Their performance is investigated in a simulation study. Applications of these methods are also illustrated with real datasets.