Model-based Direct Estimation of a Small Area Distribution Function
Most small area estimation (SAE) methods focus on estimation of linear parameters, for example small area means or totals, with comparatively little attention paid to estimation of small area distributions. This chapter summarizes the work of Salvati et al. on model-based direct estimator (MBDE) for the small area distribution function along with its mean squared error (MSE) estimation followed by an application to real data. In particular, it presents the use of MBDE for the estimation of gender-wise distribution of equivalized income and the Head Count Ratio (HCR) in the Toscana, Lombardia and Campania provinces of Italy. Then, the chapter introduces the concept of calibrated sample weights for a finite, population distribution function and then defines the MBDE estimator for this function and its, -QMSE estimator. The MBDE theory is illustrated by using it to estimate the gender-specific distribution of equivalized income in the Italian provinces.