Nonparametric Small Area Estimation via M-quantile Regression using Penalized Splines
نویسنده
چکیده
The demand of reliable statistics for small areas, when only reduced sizes of the samples are available, has promoted the development of small area estimation methods. In particular, an approach that is now widely used is based on linear mixed models. Chambers & Tzavidis (2006) have recently proposed an approach for small area estimation that is based on M-quantile models. However, when the functional form of the relationship between the qth quantile and the covariates is not linear, it can lead to biased estimators of the small area parameters. In this paper a small area mean estimator and its mean squared error estimator are proposed allowing non linearities in the relationship between the quantiles of the distribution of the study variable and the auxiliary covariates by using a nonparametric specification of the conditional Mquantile of the response variable given the covariates (Pratesi et al., 2006). Simulation studies are presented that show the finite sample properties of the proposed estimation technique.
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