https://hdl.handle.net/11000/459 Fri, 09 Oct 2026 15:18:54 GMT 2026-10-09T15:18:54Z https://hdl.handle.net/11000/40943 Título : From Calmness to Hoffman Constants for Linear Semi-infinite Inequality Systems Autor : Camacho Moro, Jesús; Cánovas Cánovas, María Josefa; Parra, Juan Resumen : In this paper we focus on different---global, semilocal, and local---versions of Hoffman-type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces, and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand sides. The Hoffman modulus is shown to coincide with the Lipschitz upper semicontinuity modulus and the supremum of calmness moduli when confined to multifunctions with a convex graph and closed images in a reflexive Banach space, which is the case for our feasible set mapping. Moreover, for this particular multifunction a formula---involving only the system's left-hand side---of the global Hoffman constant is derived, providing a generalization to our semi-infinite context of finite counterparts developed in the literature. In the particular case of locally polyhedral systems, the paper also provides a point-based formula for the (semilocal) Hoffman modulus in terms of the calmness moduli at certain feasible points (extreme points when the nominal feasible set contains no lines), yielding a practically tractable expression for finite systems. Wed, 07 Oct 2026 07:23:00 GMT https://hdl.handle.net/11000/40943 2026-10-07T07:23:00Z https://hdl.handle.net/11000/40942 Título : Feasibility problems via paramonotone operators in a convex setting Autor : Camacho Moro, Jesús; Cánovas Cánovas, María Josefa; Martínez Legaz, Juan Enrique; Parra, Juan Resumen : This paper is focussed on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it shows that operators that are simultaneously paramonotone and bimonotone are constant on their domains, and this fact is applied to tackle two particular situations. The first one, closely related to simultaneous projections, deals with a finite amount of convex sets with an empty intersection and tackles the problem of finding the smallest perturbations (in the sense of translations) of these sets to reach a nonempty intersection. The second is focussed on the distance to feasibility; specifically, given an inconsistent convex inequality system, our goal is to compute/estimate the smallest right-hand side perturbations that reach feasibility. We advance that this work derives lower and upper estimates of such a distance, which become the exact value when confined to linear systems. Wed, 07 Oct 2026 07:22:12 GMT https://hdl.handle.net/11000/40942 2026-10-07T07:22:12Z https://hdl.handle.net/11000/40904 Título : Lipschitz upper semicontinuity of linear inequality systems under full perturbations Autor : Camacho Moro, Jesús; Cánovas Cánovas, María Josefa; Gfrerer, Helmut; Parra López, Juan Resumen : The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems, i.e. where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full versus RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [On approximate solutions of systems of linear inequalities. J Res Natl Bur Stand. 1952;49:263–265] and Robinson [Some continuity properties of polyhedral multifunctions. Math Progr Study. 1981;14:206–214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyse the Lipschitz upper semicontinuity property and its corresponding modulus. Thu, 01 Oct 2026 09:28:06 GMT https://hdl.handle.net/11000/40904 2026-10-01T09:28:06Z https://hdl.handle.net/11000/40903 Título : Lipschitz upper semicontinuity in linear optimization via local directional convexity Autor : Camacho Moro, Jesús; Cánovas Cánovas, María Josefa; Parra López, Juan Resumen : This work is focussed on computing the Lipschitz upper semicontinuity modulus of the argmin mapping for canonically perturbed linear programs. The immediate antecedent can be traced out from Camacho J et al. [2022. From calmness to Hoffman constants for linear semi-infinite inequality systems. Available from: https://arxiv.org/pdf/2107.10000v2.pdf], devoted to the feasible set mapping. The aimed modulus is expressed in terms of a finite amount of calmness moduli, previously studied in the literature. Despite the parallelism in the results, the methodology followed in the current paper differs notably from Camacho J et al. [2022] as far as the graph of the argmin mapping is not convex; specifically, a new technique based on a certain type of local directional convexity is developed. Thu, 01 Oct 2026 09:26:03 GMT https://hdl.handle.net/11000/40903 2026-10-01T09:26:03Z 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. Thu, 24 Sep 2026 07:56:54 GMT https://hdl.handle.net/11000/40780 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. Thu, 24 Sep 2026 07:50:51 GMT https://hdl.handle.net/11000/40779 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. Thu, 24 Sep 2026 07:47:35 GMT https://hdl.handle.net/11000/40778 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. Thu, 24 Sep 2026 07:45:11 GMT https://hdl.handle.net/11000/40777 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. Thu, 24 Sep 2026 07:43:56 GMT https://hdl.handle.net/11000/40776 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. Tue, 22 Sep 2026 07:18:48 GMT https://hdl.handle.net/11000/40726 2026-09-22T07:18:48Z