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Summary Model-based small area estimation relies on mixed effects regression models that link the small areas and borrow strength from similar domains. When the auxiliary variables that are used in the models are measured with error, small area estimators that ignore the measurement error may be worse than direct estimators. Alternative small area estimators accounting for measurement error have been proposed in the literature but only for continuous auxiliary variables. Adopting a Bayesian approach, we extend the unit level model to account for measurement error in both continuous and categorical covariates. For the discrete variables we model the misclassification probabilities and estimate them jointly with all the unknown model parameters. We test our model through a simulation study. The effect of the model proposed is emphasized through application to data from the Ethiopia Demographic and Health Survey where we focus on the women’s malnutrition issue: a dramatic problem in developing countries and an important indicator of the socio-economic progress of a country.

Statistical agencies and other institutions collect data under the promise to protect the confidentiality of respondents. When releasing microdata samples, the risk that records can be identified must be assessed. To this aim, a widely adopted approach is to isolate categorical variables key to the identification and analyze multi-way contingency tables of such variables. Common disclosure risk measures focus on sample unique cells in these tables and adopt parametric log-linear models as the standard statistical tools for the problem. Such models often have to deal with large and extremely sparse tables that pose a number of challenges to risk estimation. This paper proposes to overcome these problems by studying nonparametric alternatives based on Dirichlet process random effects. The main finding is that the inclusion of such random effects allows us to reduce considerably the number of fixed effects required to achieve reliable risk estimates. This is studied on applications to real data, suggesting, in particular, that our mixed models with main effects only produce roughly equivalent estimates compared to the all two-way interactions models, and are effective in defusing potential shortcomings of traditional log-linear models. This paper adopts a fully Bayesian approach that accounts for all sources of uncertainty, including that about the population frequencies, and supplies unconditional (posterior) variances and credible intervals., Published at http://dx.doi.org/10.1214/15-AOAS807 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

National statistical institutes routinely apply imputation methods based on statistical models to survey nonresponses. This area of research is very important because it is at the basis of the production of economic data which are as accurate as possible. The idea is to take stock of the experiences gathered in the field of imputation methodology and to try to bridge the gap between this area of research and statistical disclosure limitation. In this paper we review our experiences on model based disclosure limitation techniques. In general, these techniques substitute the observed value of a certain variable with the estimated value via a statistical model. In particular, we discuss the problems encountered and the possible solutions found with two different models: a regression tree model [2] for a categorical variable [17] and a hierarchical model for a continuous variable [9].

Statistical Institutes as well as other data providers must comply with the obligation to preserve the privacy of respondents. Publication of files of microdata makes it possible for a malicious user to link one or more records in the released data to one or more records in the population, by combining information from external sources with the published data. Before publication, a careful risk assessment should be performed that allows to protect records through suitable utility preserving techniques. We define the disclosure risk as the probability of a correct record reidentification; for most population surveys, identification can be based on categorical variables such as place of residence, sex, age also known as key variables.