Bayesian Small Area Estimation for Skewed Business Survey Variables

Abstract

Summary In business surveys, estimates of means and totals for subnational regions, industries and business classes can be too imprecise because of the small sample sizes that are available for subpopulations. We propose a small area technique for the estimation of totals for skewed target variables, which are typical of business data. We adopt a Bayesian approach to inference. We specify a prior distribution for the random effects based on the idea of local shrinkage, which is suitable when auxiliary variables with strong predictive power are available: another feature that is often displayed by business survey data. This flexible modelling of random effects leads to predictions in agreement with those based on global shrinkage for most of the areas, but enables us to obtain less shrunken and thereby less biased estimates for areas characterized by large model residuals. We discuss an application based on data from the Italian survey on small and medium enterprises. By means of a simulation exercise, we explore the frequentist properties of the estimators proposed. They are good, and differently from methods based on global shrinkage remain so also for areas characterized by large model residuals.

Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable

“…This prior setting is not new to the literature as it was introduced by Griffin and Brown ( 2010 ) as prior for the coefficients of a linear model. Frühwirth-Schnatter and Wagner ( 2011 ) and Fabrizi et al ( 2018 ) already use this distribution as prior for random intercepts. They note that these priors encourage shrinkage of the random intercepts toward the general intercept and more so as gets smaller.…”

Robust Estimation for Small Domains in Business Surveys

“…In this paper, we have illustrated the effects of robust unit‐level models as the basis for SAE for business surveys with variables with skewed distributions; this contrasts with the adaptation of area‐level models to business surveys in Ferrante & Pacei (2017) and Fabrizi et al (2018). M‐quantile methods which deal with outlying observations provide a strategy for small domain estimation which offers much reduced rmses over direct estimation when domains are small, and better properties than other robust small area methods in this example.…”

Multilevel Time Series Modelling of Mobility Trends in the Netherlands for Small Domains

“…The Laplace and particularly the horseshoe distribution have the additional property that they shrink noisy effects more strongly towards zero. These non-normal distributions are implemented in a global-local shrinkage prior framework, similar to that described in Fabrizi et al (2018), except that we use different mixing distributions for the local scale parameters of the conditional normal distributions. The Studentt, horseshoe and Laplace random effect distributions are obtained as the marginal distributions in the case of inverse chi-squared, exponential and beta-prime mixing distributions on the local variance parameters, respectively, see for example, Polson and Scott (2010).…”

“…The second term on the right-hand side accomplishes a small bias correction, see the Supplement for a motivation. For the log transformation, the back-transforming for ̃ (r) to the original scale including bias correction (Fabrizi et al, 2018) is obtained with…”

“…Such distributions can be represented in terms of global–local shrinkage priors (Carvalho et al., 2010), which have been applied in a small area estimation context in Fabrizi et al. (2018) and Tang et al. (2018).…”