**Jornada de estimación en áreas pequeñas y modelos mixtos**

**SPAINSAE2019 – Elche 9-12 de mayo**

## Comunicaciones

**Talk 1**

**Author 1: **Isabel Molina

**Title:** Poverty mapping in small areas under informative probability sampling

**Co-authors:** Isabel Molina, María Guadarrama and J.N.K. Rao

**Abstract:** Pfeffermann and Sverchkov (2007, JASA) propose a method for estimation under informative probability sampling within the areas and spell out the proposed estimators for estimation of small area means. We extend the procedure to estimation of poverty incidences and gaps in small areas.

**Talk 2**

**Author 2: **M. Esther López Vizcaíno

**Title:** Small area estimation of household expenditures based on a bivariate nested error regression model.

**Co-authors:** M. Esther López Vizcaíno, Mª Dolores Esteban Lefler, Mª José Lombardía Cortiña, Domingo Morales González, Agustín Pérez Martín.

**Abstract:** The Spanish Household Budget Survey is annually carried out by the “Instituto Nacional de Estadística (INE)”, with the objective of obtaining information on the nature and destination of consumption expenses, as well as on various characteristics related to the conditions of household life. The main objective of this work is to estimate averages and ratios of household expenditures, in food, housing, leisure and others, by Spanish provinces. To carry out these estimations, we use a bivariate nested error regression model for small areas. Based on the selected model, we calculate the empirical best linear unbiased predictors of the target parameters by provinces. The mean squared error is analytically approximated and an explicit-formula estimator is derived. All this is validated in a complete simulation study. Finally, some maps of averages and ratios of household expenditures by Spanish provinces is given.

**Talk 3**

**Author 3: **Domingo Morales González

**Title:** Small area estimation under a measurement error bivariate Fay-Herriot model.

**Co-authors:** Jan Pablo Burgard, María Dolores Esteban, Domingo Morales, Agustín Pérez.

**Abstract:** The bivariate Fay-Herriot model is an area-level linear mixed model that can be used for estimating the domain means of two correlated target variables. Under this model, the dependent variables are direct estimators calculated from survey data and the auxiliary variables are true domain means obtained from external data sources. Administrative registers do not always give good auxiliary variables, so that statisticians sometimes take them from alternative surveys and therefore they are measured with error. We introduce a variant of the bivariate Fay-Herriot model that takes into account the measurement error of the auxiliary variables and we give fitting algorithms to estimate the model parameters. Based on the new model, we introduce empirical best predictors of domain means and we propose a parametric bootstrap procedure for estimating the mean squared error. We finally give an application to estimate poverty proportions and gaps in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.

**Talk 4:**

**Author 4: **Tomas Hobza

**Title:** Three types of unit-level gamma mixed models for small area estimation.

**Co-authors:** Tomas Hobza, Yolanda Marhuenda, Domingo Morales.

**Abstract: **Estimation of a given function of an income variable, like e.g. average incomes or poverty proportions, is considered. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variables, a first option is to apply transformations that approach normality. A second option is to use non-symmetric distributions like the gamma distribution. This contribution proposes three types of unit-level gamma mixed models for modelling positive variables and derives three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The mean squared errors of the predictors are estimated by a parametric bootstrap. Some results of simulation experiments studying the behavior of the small area predictors and the estimator of the mean squared errors are presented. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given. In the real data application a procedure for estimating the nuisance parameters is proposed.

**Talk 5:**

**Author 5: **Ana Fernández Militino

**Title:** Remote Sensing Data for Small Area Estimation.

**Co-authors: **A.F. Militino, M.D. Ugarte, U. Pérez-Goya, M. Montesino.

**Abstract: **Free access of satellite imagery provides large amounts of daily remote sensing data that can be used not only in environmental sciences, agriculture, forestry, geology or hydrology, but also in disease mapping or economic regional planning. The goal of this work is introducing, explaining and deriving some specific R tools for using these data in small area estimation. We will mainly focus on our “RGistools” package specialized in downloading multi-temporal remote sensing data, where joining, combining or smoothing techniques are developed for improving the quality of the information.

**Talk 6:**

**Author 6: **Agustín Pérez Martín y María Dolores Esteban Lefler

**Title:** Functions apply of R for SAE.

**Co-authors:** María Dolores Esteban Lefler, Domingo Morales González, Agustín Pérez Martín.

**Abstract.** Any application to real data in small area estimation, such as simulation processes that allow to check the efficiency of the models that support them, entails the use of a multitude of loops in any programming language, and in particular in R. These loops are necessary both to perform iterative intermediate calculations according to the structure of the underlying model, and to give results of estimators for each of the proposed domains. Also, depending on the nature of the R object that is being used for calculations, the number of nested loops can grow. With this session, we intend to introduce the family of functions “apply” for functional programming functions, which allow not only to simplify programming, but also to reduce execution times considerably.

**Talk 7:**

**Author 7: **María Dolores Esteban Lefler y Agustín Pérez Martín

**Title:** R functions for direct and indirect estimation based on the sample design.

**Co-authors:** María Dolores Esteban Lefler, Domingo Morales González, Agustín Pérez Martín.

**Abstract.** This communication addresses the family of direct and indirect estimators based on the sample design distribution by creating specific R functions for its calculation. In addition, We presents other functions of R to calculate the estimators of the mean square errors.

**Talk 8:**

**Author 8: **Domingo Morales

**Title: **Small area estimation under unit-level temporal linear mixed models.

**Co-authors: **Domingo Morales, Laureano Santamaría.

**Abstract. **This communication investigates the use of unit-level temporal linear mixed models for estimating linear parameters. Two models are considered, with domain and domain-time random effects. The first model assumes time independency and the second one AR(1)-type time correlation. A Fisher-scoring algorithm is used to calculate the residual maximum likelihood estimators of the model parameters. Based on the introduced models, empirical best linear unbiased predictors of small area linear parameters are studied, and analytic estimators for evaluating the performance of their mean squared errors are proposed. By using data of the Spanish surveys of income and living conditions of 2004-2008, an application to the estimation of 2008 average normalized net annual incomes in Spanish provinces by sex is given.