## Small Area Estimation

**Small Area Estimation Research**

Small area estimation (SAE) is a branch of mathematical statistics which deals with the problem of estimating population parameters in subsets (called areas or domains) of a population where the sample sizes are not large enough to provide reliable direct estimates. For this purpose, SAE introduces statistical models that “borrow strength” from related small areas, data from external sources such as large sample surveys, recent census or current administrative records or data from different time periods. The information obtained by SAE methods can be used in regional and urban planning, allocation of funds in many government programs covering education, public health, poverty etc. or in the so called disease mapping when small area techniques are used to predict disease incidence over different small areas.

Our research team is interested in model-based approach to SAE and develops methods for small area estimation based on statistical models such as linear mixed models and nested error regression models in the case of normal data or generalized linear mixed models in the case of binary, count or asymmetric data. We propose generalizations of the mentioned models to SAE problems and derive formulas and algorithms for prediction of the characteristic of interest (area means, area totals, area quantiles, etc.). Special attention is paid to estimation of the mean squared error of the predictors since such a measure of accuracy is needed in practical applications. In addition, we deal with the problems of robust estimation and outlier detection in generalized linear models.

An important part of developing a new model is to design and carry out simulation experiments studying small sample size behavior of the new methods and comparing them with the existing ones if there are any available. It means that development of non-trivial software tools is an integral part of our work since the standard statistical packages cannot be used for the studied models and moreover Monte Carlo approximation methods must often be used. Further, to show applicability and benefits of the proposed methods in practice, real data applications are performed.

**Members**

**Tomáš Hobza**

**associate professor at FNSPE CTU in Prague**

- model-based methods for small area estimation

robust estimators in generalized linear models

**Graduates**

**Petr Bohuslav**

(robust estimates in generalized linear models)

**Jaroslav Klika**

(parameter estimation in generalized linear mixed models)

**Aleš Tygl**

(comparison of two approaches to small area parameters estimation)

**Jana Hradilová**

(random regression coefficient area models)

**Jan Grebler**

(robust variants of divergence estimates)

**Tomáš Košlab**

(generalized linear mixed models for small area estimation)

**Jana Novotná**

(robust parameter estimators in a logistic regression model)

**Ondřej Faltys**

(SAE models for asymmetric data)

**Cooperation**

- Prof.
**Domingo Morales**(Uni. Miguel Hernández de Elche, Spain) - Prof.
**Leandro Pardo**(Universisad Complutense, Madrid, Spain) - Prof.
**María del Carmen Pardo**(Universisad Complutense, Madrid, Spain)

**Significant papers**

- Faltys, O., Hobza, T., Morales, D. (2021). Small area estimation under area-level generalized linear mixed models. Communications in Statistics – Simulation and Computation. DOI: 10.1080/03610918.2020.1836216.
- Morales, D., Esteban, M.D., Pérez, A., Hobza, T. (2021). A Course on Small Area Estimation and Mixed Models – Methods, Theory and Applications in R. Springer, Cham.
- Hobza, T., Marhuenda, Y., Morales, D. (2020). Small area estimation of additive parameters under unit-level generalized linear mixed models. SORT, 44(1), pp. 3-38.
- Hobza, T., Morales, D., Santamaría, L. (2018). Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models. TEST, 27(2), pp. 270-294.
- Hobza, T., Martín, N., Pardo, L. (2017). A Wald-type test statistic based on robust modified median estimator in logistic regression models. Journal of Statistical Computation and Simulation, 87(12), pp. 2309-2333.
- Hobza, T., Morales, D. (2016). Empirical best prediction under unit-level logit mixed models. Journal of Official Statistics, 32(3), pp. 661-692.
- Pardo, M.C., Hobza, T. (2014). Outlier detection method in GEEs. Biometrical Journal, 56(5), pp. 838-850.
- Hobza, T., Morales, D., Pardo, L. (2014). Divergence-based tests of homogeneity for spatial data. Statistical Papers, 55(4), pp. 1059-1077.
- Hobza, T. and Morales, D. (2013). Small area estimation under random regression coefficient models. Journal of Statistical Computation and Simulation, 83(11), pp. 2160-2177.
- Esteban, M.D., Herrador, M., Hobza, T., Morales, D. (2013). A modified nested-error regression model for small area estimation. Statistics: A Journal of Theoretical and Applied Statistics, 47(2), pp. 258-273.