Small area estimation using a nonparametric model-based direct estimator
Nonparametric regression is widely used as a method of characterizing a non-linearrelationship between a variable of interest and a set of covariates. Practical application ofnonparametric 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 amodel that combines a penalized spline (p-spline) fit and random area effects. The conceptof model-based direct estimation is used to develop an alternative nonparametric approachto estimation of a small area mean. The suggested estimator is a weighted average of thesample values from the area, with weights derived from a linear regression model withrandom area effects extended 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 theproposed model-based direct estimator and its associated mean squared error estimatorperform well. They are worth considering in small area estimation applications wherethe underlying population regression relationships are non-linear or have a complicatedfunctional form.