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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.

In this paper we focus on small area models with measurement error in covariates. Based on data from the Measuring Morality study, a nationally representative survey of United States residents, that contains a validated behavioural measure of generosity (the dictator game) along with the household income of respondents, we define a measurement error model suitable to obtain area-level estimates of generosity at the district level. We investigate the effect of introducing the measurement error in this model, focusing on fully Bayesian as well as Empirical Bayesian (EB) estimation proposed in the recent literature. We discuss the characteristics of each of the two approaches and analyze the impact of the measurement error on the resulting estimates based on real data and a simulation study.

Besides health and socio-economic status, the social relationships maintained during elderly play an important role in shaping the living conditions at older ages. In this part of life, the family represents the major framework in which interpersonal relationships are experienced. With population ageing, the family increasingly ensures elderly care, especially where targeted public policies are lacking, and its protective effect on survival is foreseen. In this paper we investigate the complex role of family in mortality and contribute to the debate on the ideal living condition for elderly people, exploiting a nationwide integrated survey on private and collective households in France. Following a cohort of 16,263 individuals aged 55, we investigate the effect of family relations on survival. We question whether the lack of family care connected with the absence of active relationships with family members may be at least partly compensated by institutional settings. Estimates of life expectancy show that at the age of 60, people living in institutions live on average 10 years less that those living in private households, the gap decreasing with age. Cox proportional hazards models show a protective role of children on mortality. Having no children seems to be associated with a lower risk of death, but the effect is significant only for those declaring rare or no contacts with their children. Survival analysis also suggests that institutional living arrangement may be protective for the most fragile individuals, namely the severely disabled, isolated persons.

In survey sampling, interest often lies in unplanned domains (or small areas), whose sample sizes may be too small to allow for accurate design-based inference. To improve the direct estimates by borrowing strength from similar domains, most small area methods rely on mixed effects regression models. ¶ This contribution extends the well known Fay–Herriot model (Fay and Herriot, 1979) within a Bayesian approach in two directions. First, the default normality assumption for the random effects is replaced by a nonparametric specification using a Dirichlet process. Second, uncertainty on variances is explicitly introduced, recognizing the fact that they are actually estimated from survey data. The proposed approach shrinks variances as well as means, and accounts for all sources of uncertainty. Adopting a flexible model for the random effects allows to accommodate outliers and vary the borrowing of strength by identifying local neighbourhoods where the exchangeability assumption holds. Through application to real and simulated data, we investigate the performance of the proposed model in predicting the domain means under different distributional assumptions. We also focus on the construction of credible intervals for the area means, a topic that has received less attention in the literature. Frequentist properties such as mean squared prediction error (MSPE), coverage and interval length are investigated. The experiments performed seem to indicate that inferences under the proposed model are characterised by smaller mean squared error than competing approaches; frequentist coverage of the credible intervals is close to nominal.

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)

The paper proposes a new disclosure limitation procedure based on simulation. The key feature of the proposal is to protect actual microdata by drawing artificial units from a probability model, that is estimated from the observed data. Such a model is designed to maintain selected characteristics of the empirical distribution, thus providing a partial representation of the latter. The characteristics we focus on are the expected values of a set of functionss these are constrained to be equal to their corresponding sample averagess the simulated data, then, reproduce on average the sample characteristics. If the set of constraints covers the parameters of interest of a user, information loss is controlled for, while, as the model does not preserve individual values, re-identification attempts are impaired-synthetic individuals correspond to actual respondents with very low probability. Disclosure is mainly discussed from the viewpoint of record re-identification. According to this definition, as the pledge for confidentiality only involves the actual respondents, release of synthetic units should in principle rule out the concern for confidentiality. The simulation model is built on the Italian sample from the Community Innovation Survey (CIS). The approach can be applied in more generality, and especially suits quantitative traits. The model has a semi-parametric component, based on the maximum entropy principle, and, here, a parametric component, based on regression. The maximum entropy principle is exploited to match data traitss moreover, entropy measures uncertainty of a distribution: its maximisation leads to a distribution which is consistent with the given information but is maximally noncommittal with regard to missing information. Application results reveal that the fixed characteristics are sustained, and other features such as marginal distributions are well represented. Model specification is clearly a major points related issues are selection of characteristics, goodness of fit and strength of dependence relations.

Small area estimation concerns the problem of releasing estimates for domains that are not planned by design in statistical surveys. For such domains the observed sample size may often be too small to allow for accurate estimation of aggregates of interest. To borrow strength from related domains, the vast majority of small area models relies on mixed effects regression models. Whereas inference on the fixed effects is shown to be robust to deviations from normality, estimation of the random effects is crucial for predicting small area quantities. The potential impact of distributional assumptions on the random effects is shown to be important; missing covariates can lead to multimodal distributions for the random effects; the latter may also be skewed. Any parametric assumption, applying to nonobservable quantities, is difficult to check. This contribution examines a Bayesian semiparametric version of the Fay–Herriot model in which the default normality assumption for the random effects is replaced by a nonparametric specification, based on the Dirichlet process. Viability of the approach and the effect of introducing a flexible specification of the random effects are investigated through an application to simulated data.

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.

In this paper we define a proposal for an alternative data dissemination strategy of the Italian Household Expenditure Survey (HES). The proposal moves from partitioning the set of users in different groups homogeneous in terms of needs, type of statistical analyses and access to external information. Such a partition allows the release of different data products that are hierarchical in information content and that may be protected using different data disclosure limitation methods. A new masking procedure that combines Migroaggregation and Data Swapping is proposed to preserve sampling weights.

The release of survey microdata files requires a preliminary assessment of the disclosure risk of the data. Record-level risk measures can be useful for “local” protection (e.g. partially synthetic data [21], or local suppression [25]), and are also used in [22] and [16] to produce global risk measures [13] useful to assess data release. Whereas different proposals to estimating such risk measures are available in the literature, so far only a few attempts have been targeted to the evaluation of the statistical properties of these estimators. In this paper we pursue a simulation study that aims to evaluate the statistical properties of risk estimators. Besides presenting results about the Benedetti-Franconi individual risk estimator (see [11]), we also propose a strategy to produce improved risk estimates, and assess the latter by simulation. The problem of estimating per record reidentification risk enjoys many similarities with that of small area estimation (see [19]): we propose to introduce external information, arising from a previous census, in risk estimation. To achieve this we consider a simple strategy, namely Structure Preserving Estimation (SPREE) of Purcell and Kish [18], and show by simulation that this procedure provides better estimates of the individual risk of reidentification disclosure, especially for records whose risk is high.

We argue that any microdata protection strategy is based on a formal reference model. The extent of model specification yields "parametric", "semiparametric", or "nonparametric" strategies. Following this classification, a parametric probability model, such as a normal regression model, or a multivariate distribution for simulation can be specified. Matrix masking (Cox [2]), covering local suppression, coarsening, microaggregation (Domingo-Ferrer [8]), noise injection, perturbation (e.g. Kim [15]; Fuller [12]), provides examples of the second and third class of models. Finally, a nonparametric approach, e.g. use of bootstrap procedures for generating synthetic microdata (e.g. Dandekar et. al. [4]) can be adopted.In this paper we discuss the application of a regression based imputation procedure for business microdata to the Italian sample from the Community Innovation Survey. A set of regressions (Franconi and Stander [11]) is used for generating flexible perturbation, for the protection varies according to identifiability of the enterprise; a spatial aggregation strategy is also proposed, based on principal components analysis. The inferential usefulness of the released data and the protection achieved by the strategy are evaluated.