Small area estimation using a nonparametric model-based direct estimator

Nonparametric regression is widely used as a method of characterising a non-linear relationship between a variable of interest and a set of covariates. Practical application of nonparametric regression methods in the field of small area estimation is fairly recent, and has so far focussed on the use of empirical best linear unbiased prediction under a model that combines a penalized spline (p-spline) fit and random area effects. In this paper, we propose an alternative approach to using nonparametric regression to estimate a small area mean, based on application of the recently introduced concept of model-based direct estimation. Under this approach, the estimator of the small area mean is a weighted average of the sample values from the area, with weights derived from an appropriately specified linear regression model with random area effects. Here we extend this model to incorporate a smooth, nonparametrically specified trend. Estimation of the mean squared error of the proposed small area estimator is also discussed. Monte Carlo simulations based on both simulated and real datasets show that the proposed model-based direct estimator and its associated mean squared error estimator perform well and are worth considering in small area estimation applications where the underlying population regression relationships are non-linear or have a complicated functional form.