Local polynomial inference for small area statistics: estimation, validation and prediction

Abstract

Small area statistics has received considerable attention in the last two decades from both public and private sectors. More recently, semiparametric mixed-effects models have been proposed for a more flexible modelling. Surprisingly, although model specification testing is of particular importance in small area statistics, this has been less explored. Its importance is based on the fact that small area statistics applies model-based estimation and prediction. Local polynomials can nest typically used parametric models without bias – independent of the smoothing parameter – and are therefore particularly useful in practice. First, estimation and testing with local polynomials is introduced for mixed-effects models. Several extensions for further structural modelling with dimension-reducing effects are discussed. Second, different computationally attractive specification tests are proposed and compared. The methods are compared along simulation studies. Its usefulness is underpinned by the small-area regression problems of forest stand and farm production.

Keywords:

• semiparametric small area statistics
• mixed-effects models
• model specification tests
• local polynomial estimation
• small area statistics
• specification testing

AMS Subject Classification :

• 62G08
• 62H15
• 62P12

Acknowledgements

The authors gratefully acknowledge the financial support of the Spanish ‘Ministerio de Ciencia e Innovación’ MTM2008-03010, the Xunta de Galicia PGIDIT06PXIB207009PR, the Belgian network IAP-Network P6/03, and the Deutsche Forschungsgemeinschaft FOR916. We further thank two anonymous referees and the editor for helpful discussion and remarks.

Notes

In Galician herbceous cultivation, fallow lands, family gardens cultivos herbáceos, barbeitos, hortas familiares, which thus include fields that are left fallow, and large family (vegetable but not fruit) gardens.