Small area estimation on poverty indicators

We propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.Empirical best estimator, Parametric bootstrap, Poverty mapping, Small area estimation

Small area estimation on poverty indicators

We propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains

Small area estimation of general parameters under complex sampling designs

When the probabilities of selecting the individuals for the sample depend on the outcome values, we say that the selection mechanism is informative. Under informative selection, individuals with certain outcome values appear more often in the sample and therefore the sample is not representative of the population. As a consequence, usual model-based inference based on the actual sample without appropriate weighting might be strongly biased. For estimation of general non-linear parameters in small areas, we propose a model-based pseudo empirical best (PEB) method that incorporates the sampling weights and reduces considerably the bias of the unweighted empirical best (EB) estimators under informative selection mechanisms. We analyze the properties of this new method in simulation experiments carried out under complex sampling designs, including informative selection. Our results confirm that the proposed weighted PEB estimators perform significantly better than the unweighted EB estimators in terms of bias under informative sampling, and compare favorably under non-informative sampling. In an application to poverty mapping in Spain, we compare the proposed weighted PEB estimators with the unweighted EB analogues.Acknowledgements: the second author acknowledge financial support from the Spanish Ministry of Education and Science, research project MTM2015-64842-P

My Chancy Life as a Statistician

In this short article, I will attempt to provide some highlights of my chancy life as a statistician in chronological order spanning over 60 years, 1954 to present

Jackknife variance estimation for multivariate statistics under hot-deck imputation from common donors

We consider a survey setting where missing values in a bivariate dataset are imputed by a hot-deck procedure which imputes all missing values for a given unit from a common donor with complete responses. It is shown that such an imputation procedure may lead to bias in standard estimators and a bias-adjusted estimator is derived. The variances of both the standard estimators and the bias-adjusted estimator are evaluated and jackknife variance estimators for each are constructed. We demonstrate the asymptotic unbiasedness of these variance estimators and illustrate their behaviour in a small simulation study

Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method

Model-based estimation of small area means can lead to reliable estimates when the area sample sizes are small. This is accomplished by borrowing strength across related areas using models linking area means to related covariates and random area effects. The effective selection of variables to be included in the linking model is important in small area estimation. The main purpose of this paper is to extend the earlier work on variable selection for area level and two-fold subarea level models to three-fold sub-subarea models linking sub-subarea means to related covariates and random effects at the area, sub-area, and sub-subarea levels. The proposed variable selection method transforms the sub-subarea means to reduce the linking model to a standard regression model and applies commonly used criteria for variable selection, such as AIC and BIC, to the reduced model. The resulting criteria depend on the unknown sub-subarea means, which are then estimated using the sample sub-subarea means. Then, the estimated selection criteria are used for variable selection. Simulation results on the performance of the proposed variable selection method relative to methods based on area level and two-fold subarea level models are also presented

Bootstrap procedures for the pseudo empirical likelihood method in sample surveys

Pseudo empirical likelihood ratio confidence intervals for finite population parameters are based on asymptotic [chi]2 approximation to an adjusted pseudo empirical likelihood ratio statistic, with the adjustment factor related to the design effect. The calculation of the design effect involves variance estimation and hence requires second order inclusion probabilities. It also depends on how auxiliary information is used, and needs to be derived one-at-a-time for different scenarios. This paper presents bootstrap procedures for constructing pseudo empirical likelihood ratio confidence intervals. The proposed method bypasses the need for design effects and is valid under general single-stage unequal probability sampling designs with small sampling fractions. Different scenarios in using auxiliary information are handled by simply including the same type of benchmark constraints with the bootstrap procedures. Simulation results show that the bootstrap calibrated intervals perform very well and have much improved coverage probabilities over the [chi]2-based intervals when the sample sizes are small or moderate.Auxiliary information Confidence interval Design effect Profile likelihood Stratified sampling Unequal probability sampling