Robust Unit-Level Small Area Estimation: A Fast Algorithm for Large Datasets

Abstract

Small area estimation is a topic of increasing importance in official statistics. Although the classical EBLUP method is useful for estimating the small area means efficiently under the normality assumptions, it can be highly influenced by the presence of outliers. Therefore, Sinha and Rao (2009; The Canadian Journal of Statistics) proposed robust estimators/predictors for a large class of unit- and area-level models. We confine attention to the basic unit-level model and discuss a related, but slightly different, robustification. In particular, we develop a fast algorithm that avoids inversion and multiplication of large matrices, and thus permits the user to apply the method to large datasets. In addition, we derive much simpler expressions of the boundedinfluence predicting equations to robustly predict the small-area means than Sinha and Rao (2009) did.

Integrating surveys with geospatial data through small area estimation to disaggregate SDG indicators: A practical application on SDG Indicator 2.3.1

“…However, this can be relaxed by estimating the σ 2 e,d from the unit level sample data and then stabilize them by means of smoothing techniques such as the generalized variance function (GVF) approach [14]. Several extensions of the basic area level model are available in the literature and can be adopted to address special situations such as the presence of spatial [18] or spatio-temporal [19] correlation, heteroscedasticity of random effects [20], influential outliers [21], and auxiliary variables -such as those retrieved from big data sources -affected by measurement errors [22].…”

“…These extensions are particularly relevant in the context of the SDG monitoring framework, where many of the indicators are expressed as ratios and proportions. Additional extensions allow to include sampling weights in the estimation process [26], address the presence of heteroscedasticity in the error term [20], and produce estimates which are robust to influential outliers [21].…”