Estimating the percentage of food expenditure in small areas using bias-corrected PP-spline based estimators

Small area estimators based on a penalized spline regression model approximating a non-linear but smooth relationship between a response and a given covariate are obtained. In each small area, individual curves are fitted using penalized splines with BB-spline bases, exploiting the mixed model representation of the PP-splines for inferential purposes. To account for possible bias, a design-oriented bootstrap correction is proposed. The mean squared error of the bias-corrected estimator is also provided. The methods are used to estimate the percentage of food expenditure for alternative household sizes at provincial level in Spain using the 2006 Spanish Household Budget Survey.