Small Area Models for Skewed Brazilian Business Survey Data

Abstract

Summary The Brazilian Institute of Geography and Statistics performs an annual service survey that focuses on segments of the tertiary sector. Sample estimates for some economic activities in the north, north‐east and midwest regions of Brazil have low precision due to the sample design. Furthermore, one of the main variables of interest is considerably skewed with potential outliers. To overcome this problem, skew normal and skew t‐models are proposed to produce model‐based estimates. The small domain estimation models relate operating revenue variables to potential auxiliary variables (the number of employed people and wages) obtained from a business register. The models proposed are compared with the usual Fay–Herriot model under the assumptions of known and unknown sampling variances and its transformed log‐version under the assumption of known variances. The evaluation studies with real business survey data show that the models proposed seem to be more efficient for small area predictions under skewed data than the customarily employed Fay–Herriot model, as well as its log‐normal version.

Skew normal small area time models for the Brazilian annual service sector survey

“…However, while the lognormal model makes the asymmetry hypothesis more plausible, an exponential function is required when estimates are converted to the original scale, increasing the variability of the estimates. Moreover, Moura et al (2017) found that the lognormal model performs less well than the skew normal model in their application to BASSS data. Azzalini (1985) described the family of skew normal distributions that preserve some properties of the normal distribution except for the parameter that regulates the distribution's asymmetry.…”

“…sampling unit level since aggregated data are more accessible and are less subjected to statistical confidentiality restrictions. However, as pointed out by Moura et al (2017), the Fay-Herriot model assumes conditional normality of the direct estimator which is not suitable for fitting skewed data, particularly for domains with very small sample sizes. Neves et al (2013) developed the first small domain estimation approach for Brazilian economic surveys.…”

“…They successfully fitted the skew normal model to head-of-household mean income for 140 enumeration areas in the scope of an experimental Brazilian demographic census. Moura et al (2017) compared different small area approaches for fitting skewed data using real business survey data. It was the first experiment in which skew normal models in a Bayesian framework were tested to produce small area estimates for the Brazilian Annual Service Sector Survey (BASSS).…”

Estimating Regional Wealth in Germany: How Different are East and West Really?

“…In this work, we propose an easy-toapply approach by using the log-transformation to meet the model assumptions. Another approach to handle skewed data could be the assumption of a skewed normal distribution in the FH model (Moura, Neves, and do N. Silva, 2017). With regards to the backtransformation, the usage of the smearing estimator proposed by Duan (1983) could be transferred to the Fay-Herriot model as Li, Liu, and Zhang (2017) use it for the nested error linear regression model.…”

Small area estimation of socioeconomic indicators for sampled and unsampled domains

“…Many extensions were made to the FH predictor to meet different practical problems. Inter alia, Prasad and Rao (1990) and Datta and Lahiri (2000) propose MSE estimators for the FH predictor, Li and Lahiri (2010) and Yoshimori and Lahiri (2014) introduce new adjusted maximum likelihood fitting methods, Jiang and Tang (2011) study the influence of the fitting algorithm in the empirical best prediction, Molina et al (2015) derive preliminary testing predictors, Moura et al (2017) modified the basic model to analyze skewed business survey data, Ybarra and Lohr (2008), Bell et al (2019), and study the effect of measurement errors in the covariates, Pratesi and Salvati (2008), Gonzáalez-Manteiga et al (2010), Articus and Burgard (2014), and Morales et al (2015) allow for a heterogeneous dependency structure in the FH model, Esteban et al (2012) and Marhuenda et al (2013) estimate small area poverty proportions under temporal and spatiotemporal Fay-Herriot models, respectively.…”