We test if a regression function belongs to a class of parametric models by measuring the discrepancy between a parametric fit and a local polynomial regression. The proposed test is a weighted L2-norm of a smoothed function based on the parametric residuals.

The prediction of vectors of small area quantities based on a multivariate Fay-Herriot model is addressed. For this, an empirical best linear unbiased predictor (EBLUP) of the target vector is used, where the model parameters are estimated by two different methods based on moments. The mean...