Robust estimation for small domains in business surveys

TL;DR

This paper evaluates robust small area estimation methods for business surveys, focusing on retail sector data in the Netherlands, and finds M-quantile estimators outperform traditional methods in accuracy and robustness.

Contribution

It introduces a doubly robust approach combining survey weights with outlier-resistant estimators for small area estimation in business statistics.

Findings

M-quantile estimators have the lowest mean squared error.

Robust methods outperform traditional estimators in the presence of influential data.

The doubly robust approach enhances estimation reliability.

Abstract

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.