Neural Networks for calibration estimation of finite population parameters

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage. Calibrating the observation weights on the population means (or totals) of the auxiliary variables implicitly assumes on a linear superpopulation regression model. When auxiliary information is available for all units in the population, more complex modeling can be handled by means of model calibration (Wu and Sitter, 2001). Generalized linear models and nonlinear models are considered, and estimation weights are sought to satisfy calibration constraints on the fitted values. In this work we introduce a new type of model calibration nonparametric estimator for the finite population mean based on neural network learning. That is, we extend model calibration by assuming more general superpopulation models and employ neural networks to obtain the fitted values to calibrate on. Under suitable regularity conditions, the proposed estimator is proved to be asymptotically design unbiased and consistent. An approximation to its mean squared error is also derived and an asymptotically design unbiased and consistent estimator of the mean squared error is then proposed.