Title: Non-linear small area models under constraints
Authors: Julian Wagner - University of Trier (Germany) [presenting]
Ralf Muennich - University of Trier (Germany)
Abstract: Small area estimation methods are applied to obtain reliable estimates for parameters of sub-populations with sub-sample sizes too small for direct estimates. Traditional small area models are based on the assumption of an approximately linear relationship within the data, which is sufficiently often violated in practice. A non-linear small area model based on spline approximation is presented, which allows for additional shape constraints on the regression function. Moreover, constraints on the small area estimates are taken into consideration leading to quadratic programming problems. The applicability of the method is shown by a practical application and the results are compared to different small area methods. Finally, an estimator of the small area prediction mean squared error is proposed and the extension of the model to a multidimensional setting is discussed.