https://hdl.handle.net/11000/459 2026-09-25T07:43:10Z https://hdl.handle.net/11000/40780 Título : Small area estimation of proportions and rates under area-level Dirichlet mixed models Autor : Cabello García, Esteban; Esteban, María Dolores; Hobza, Tomáš; Morales, Domingo; Pérez, Agustín Resumen : This paper introduces an area-level Dirichlet mixed model for predicting compositional indicators of small areas. Direct estimators of the domain category proportions of a classification variable are the target variables of the new model. Once the model has been selected and fitted to the data, predictors of proportions, totals and rates of small areas are obtained and their mean square errors are estimated by parametric bootstrap. Several simulation experiments, designed to analyse the behaviour of the fitting algorithm, the small area predictors and the bootstrap procedure, are carried out. An application to real data from the Spanish Labour Force Survey, in the last quarter of 2022, is given. The target is the estimation of proportions of employed, unemployed and inactive people and unemployment rates by province, sex and age group. 2026-09-24T07:56:54Z https://hdl.handle.net/11000/40779 Título : Three-fold Fay-Herriot model with unequal variance random effects Autor : Cabello García, Esteban; Marcis, Laura; Morales, Domingo; Pagliarella, Maria Chiara; Salvatore, Renato Resumen : This study extends the classical Fay–Herriot model to a threefold hierarchical structure incorporating heteroscedastic random effects. Three submodels are also introduced within this framework. Small area best linear unbiased predictors are derived for linear indicators, and their mean squared errors (MSEs) are estimated using both analytical and parametric bootstrap methods. Model performance and reliability are evaluated through diagnostic tools and influence measures, specifically designed for small area estimation. Simulation experiments are conducted to analyze the empirical properties of the predictors and MSE estimators. The proposed approach is applied to data from the 2019–2021 Spanish Living Conditions Survey to estimate the proportion of women and men below the poverty line, disaggregated by province, age group, and year. 2026-09-24T07:50:51Z https://hdl.handle.net/11000/40778 Título : Small area estimation of poverty indicators under bivariate Fay–Herriot model with correlated time effects Autor : Cabello García, Esteban; Esteban, María Dolores; Morales, Domingo; Pérez Martín, Agustín Resumen : This paper presents an area-level temporal bivariate linear mixed model, incorporating correlated time effects for estimating socioeconomic indicators in small areas. The model is applied through the residual maximum likelihood method, leading to the derivation of empirical best linear unbiased predictors for these indicators. Additionally, an approximation of the mean square error matrix (MSE) is provided and four MSE estimators are proposed. The first estimator involves a plug-in approach to the MSE approximation, while the remaining estimators are based on parametric bootstrap procedures. To assess the performance of the fitting algorithm, predictors, and MSE estimators, three simulation experiments are carried out. An application to real data from the 2016 to 2022 Spanish Living Conditions Survey is conducted. The focus is on estimating poverty proportions and gaps for the year 2022, categorized by provinces and sex. 2026-09-24T07:47:35Z https://hdl.handle.net/11000/40777 Título : Small area estimation of poverty proportions under heteroscedastic Fay-Herriot models Autor : Cabello García, Esteban; Esteban, María Dolores; Morales, Domingo; Pérez Martín, Agustín Resumen : This paper presents a modification of the Fay-Herriot model that does not assume the homoscedasticity hypothesis of the random effects. To do this, it linearly explains a transformation of its variance from auxiliary variables. The new heteroscedastic model is more flexible and generally allows a better fit to the data. The mathematical foundations of the model are introduced, including fitting algorithms, small area linear indicator predictors, and mean square error estimators. Through simulation experiments, the behavior of the introduced algorithms, predictors and estimators is empirically studied. An application to real data from the Spanish Living Conditions Survey of 2022 is given. The target is the estimation of domain proportions of people under the poverty threshold by province and sex. 2026-09-24T07:45:11Z https://hdl.handle.net/11000/40776 Título : Predicting gender employment discrepancies: A multivariate Fay-Herriot model for transformed proportions Autor : Cabello García, Esteban; Morales, Domingo; Pérez, Agustín Resumen : Exposure indices measure the degree of contact between two groups and are used to quantify occupational discrepancies between genders in a set of occupational sectors. This paper presents a novel methodology for predicting area-level proportions of employed men and women across various occupation sectors, along with estimating exposure indexes. The challenge arises from the compositional nature of the direct estimators of proportions, which tend to be imprecise when sample sizes are small. To overcome this problem, we propose to use a compositional multivariate Fay–Herriot model. By applying log-ratio transformations to the direct estimators of proportions, we can effectively capture the underlying structure and dependencies within the data. Small area estimators for proportions and exposure indexes are derived from the fitted model, and their corresponding root-mean-squared errors are estimated using parametric bootstrap techniques. To demonstrate the applicability of our approach, we conduct a case study using data from quarters 3 and 4 of the Spanish Labour Force Survey of 2022. The primary objective is to investigate the state of gender occupational segregation in Spanish provinces, thereby providing valuable insights into this socioeconomic phenomenon. 2026-09-24T07:43:56Z https://hdl.handle.net/11000/40726 Título : Area-Level Model-Based Small Area Estimation of Divergence Indexes in the Spanish Labour Force Survey Autor : Cabello García, Esteban; Morales, Domingo; Pérez, Agustín Resumen : This article develops model-based predictors for area-level proportions of employed men and women by occupation sectors and for entropies and divergence indexes (DIs) within and between sex groups. Since the direct estimators of the proportions add up to one in the occupational sections, they are compositions that can be imprecise if the sample sizes are small. We fit a multivariate Fay–Herriot model to logratio transformations of the direct estimators of the proportions. Small area estimators of the proportions, entropies, and DIs are derived from the fitted model and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyze the behavior of the introduced model-based predictors are carried out. We give an application to Spanish Labour Force Survey data from 2022. The target is to investigate the state of sex occupational entropies and divergences in Spanish provinces. 2026-09-22T07:18:48Z https://hdl.handle.net/11000/40718 Título : Variable selection for Fay–Herriot models: a cooperative game theory approach Autor : Cabello García, Esteban; Gonçalves Dosantos, Juan Carlos; Morales, Domingo; Sánchez Soriano, Joaquín Resumen : This paper presents a novel approach to variable selection in small area estimation, focusing on the Fay–Herriot model. Traditional methods, such as those based on Akaike and Kullback symmetric divergence information criteria, often rely on stepwise selection and focus on the complete model, without individually examining the influence of auxiliary variables. The Shapley value of cooperative game theory is proposed to measure the average importance of auxiliary variables. The Shapley value evaluates all possible combinations of auxiliary variables, ensuring an efficient average influence of the selected combination. We study its properties mathematically and investigate its performance through simulation experiments, showing consistent identification of the true generating variables even under challenging conditions. An application to the 2022 Spanish Living Conditions Survey illustrates the method’s usefulness in selecting the model on which to base predictors of poverty proportions in Spanish provinces by sex. 2026-09-18T07:29:08Z https://hdl.handle.net/11000/40717 Título : On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices Autor : Estañ, Teresa; Llorca, Natividad; Martínez Rico, Ricardo; Sánchez Soriano, Joaquín Resumen : In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not. 2026-09-18T07:27:56Z https://hdl.handle.net/11000/40716 Título : On how to allocate the fixed cost of transport systems Autor : Estañ, Teresa; Llorca, Natividad; Martínez Rico, Ricardo; Sánchez Soriano, Joaquín Resumen : In this study, we consider different cities located along a tram line. Each city may have one or several stations and information is available about the flow of passengers between any pair of stations. A fixed cost (salaries of the executive staff, repair facilities, or fixed taxes) must be divided among the cities. This cost is independent of the number of passengers and the length of the line. We propose a mathematical model to identify suitable mechanisms for sharing the fixed cost. In the proposed model, we study, and characterize axiomatically, three rules, which include the uniform split, the proportional allocation and an intermediate situation. The analyzed axioms represent the basic requirements for fairness and elemental properties of stability. 2026-09-18T07:26:09Z https://hdl.handle.net/11000/40715 Título : Does it make sense to analyse a two-sided market as a multi-choice game? Autor : Branzei, Rodica; Gutiérrez, Elisabeth; Llorca, Natividad; Sánchez Soriano, Joaquín Resumen : In this paper, we introduce the model of multi-choice two-sided market games related to two-sided market situations. Associated with them we study whether the disaggregate management of the individual units of goods provide better insights, by means of set valued solution concepts like the core that is widely used in classical and multi-choice two-sided games. We introduce the Owen core and the pairwise egalitarian contribution set in this context and analyse whether classic and multi-choice two-sided market models are equivalents in terms of these set valued solution concepts from the point of view of aggregate payoffs. The answer to this analysis is that in aggregate terms there are no significant differences between the multi-choice approach and the standard approach. However, they are not equivalent from a disaggregate perspective. 2026-09-18T07:24:53Z