  Small area (or small domain) estimation is still rarely applied in business
statistics, because of challenges arising from the skewness and variability of
variables such as turnover. We examine a range of small area estimation methods
as the basis for estimating the activity of industries within the retail sector
in the Netherlands. We use tax register data and a sampling procedure which
replicates the sampling for the retail sector of Statistics Netherlands'
Structural Business Survey as a basis for investigating the properties of small
area estimators. In particular, we consider the use of the EBLUP under a random
effects model and variations of the EBLUP derived under (a) a random effects
model that includes a complex specification for the level 1 variance and (b) a
random effects model that is fitted by using the survey weights. Although
accounting for the survey weights in estimation is important, the impact of
influential data points remains the main challenge in this case. The paper
further explores the use of outlier robust estimators in business surveys, in
particular a robust version of the EBLUP, M-regression based synthetic
estimators, and M-quantile small area estimators. The latter family of small
area estimators includes robust projective (without and with survey weights)
and robust predictive versions. M-quantile methods have the lowest empirical
mean squared error and are substantially better than direct estimators, though
there is an open question about how to choose the tuning constant for bias
adjustment in practice. The paper makes a further contribution by exploring a
doubly robust approach comprising the use of survey weights in conjunction with
outlier robust methods in small area estimation.
