Jan Pablo Burgard (Trier University), María Dolores Esteban (University Miguel Hernández of Elche), Domingo Morales (University Miguel Hernández of Elche) and Agustín Pérez (University Miguel Hernández of Elche).
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.
Keywords: Multivariate models; Fay–Herriot model; small area estimation; measurement error; Monte Carlo simulation; poverty proportion; poverty gap
Laureano F. Escudero (Rey Juan Carlos University of Madrid), M. Araceli Garín (University of País Vasco), Juan F. Monge (Miguel Hernández University of Elche) and Aitziber Unzueta (University of País Vasco).
Abstract: Two matheuristic decomposition algorithms are introduced. The ﬁrst one is a Progressive Hedging type so-named Regularized scenario Cluster Progressive Algorithm. The second one is a Frank-Wolfe PH type so-named Regularized scenario Cluster Simplicial Decomposition Progressive Algorithm. An extension of endogenous Type III uncertainty is considered for representing the decision dependent scenario probability and outlook. Its performance is tested in the time-consistent Expected Conditional Stochastic Dominance risk averse environment. As a result of the modeling, the typical risk neutral multistage mixed 0–1 linear stochastic problem under uncertainty is replaced with an enlarged model that is equivalent to the required mixed 0–1 bilinear model. Based on the special features of the problem, it is unrealistic to seek the optimal solution for large-scale instances. Feasible solutions and lower bounds on the solution value of the original model are provided. In total, 48 strategies are considered, each one consists of a combination of a regularization norm, a calibration type for the PH pseudo-gradient computation, and a set of value intervals of the inﬂuential variables on a representative endogenous uncertainty-based piecewise function in the scenarios. Computational results are reported for a large-scale extension of a well-known real-life pilot case for preparedness resource allocation planning aiming to natural disaster relief. The matheuristics outperform the plain use of a state-of-the-art solver.
Keywords: Stochastic programming; Exogenous and endogenous uncertainties; Time-consistent stochastic dominance; Mixed 0–1 bilinear optimization; Scenario cluster-based decomposition algorithms
Manuel Franco (University of Murcia), Juana María Vivo (University of Murcia), Manuel Quesada-Martínez (Miguel Hernández University), Astrid Duque-Ramos (University of Antioquia) and Jesualdo Tomás Fernández-Breis (University of Murcia).
Abstract: The development and application of biological ontologies have increased significantly in recent years. These ontologies can be retrieved from different repositories, which do not provide much information about quality aspects of the ontologies. In the past years, some ontology structural metrics have been proposed, but their validity as measurement instrument has not been sufficiently studied to date. In this work, we evaluate a set of reproducible and objective ontology structural metrics. Given the lack of standard methods for this purpose, we have applied an evaluation method based on the stability and goodness of the classifications of ontologies produced by each metric on an ontology corpus. The evaluation has been done using ontology repositories as corpora. More concretely, we have used 119 ontologies from the OBO Foundry repository and 78 ontologies from AgroPortal. First, we study the correlations between the metrics. Second, we study whether the clusters for a given metric are stable and have a good structure. The results show that the existing correlations are not biasing the evaluation, there are no metrics generating unstable clusterings and all the metrics evaluated provide at least reasonable clustering structure. Furthermore, our work permits to review and suggest the most reliable ontology structural metrics in terms of stability and goodness of their classifications.
Keywords: biological ontologies; quantitative metrics; metrics comparison; data analysis.
Rocío Hernández-Sanjaime (University Miguel Hernández of Elche), Martín González (University Miguel Hernández of Elche) and Jose J. López-Espín (University Miguel Hernández of Elche)
Abstract: Conventional simultaneous equation models assume that the error terms are serially independent. In some situations, data may present hierarchical or grouped structure and this assumption may be invalid. A new multivariate model referred as to Multilevel Simultaneous Equation Model (MSEM) is developed under this motivation. The maximum likelihood estimation of the parameters of an MSEM is considered. A matrix-valued distribution, namely, the matrix normal distribution, is introduced to incorporate an among-row and an among-column covariance matrix structure in the specification of the model. In the absence of an analytical solution of the system of likelihood equations, a general-purpose optimization solver is employed to obtain the maximum likelihood estimators. In a first approach to the solution of the problem, the adequacy of the matrix normal distribution is evaluated empirically in the case in which the double covariance structure is known. Using simulated data under the model assumptions, the performance of the maximum likelihood estimator (MLE) is assessed with regard to other conventional alternatives such as two-stage least squares estimator (2SLS).
Keywords: Multilevel simultaneous equation model; Maximum likelihood estimation; Matrix normal distribution; Simultaneous equation model; Multilevel model
Gustavo Bergantiños (University of Vigo), María Gómez-Rúaa (University of Vigo), Natividad Llorca (University Miguel Hernández of Elche), Manuel Pulido (University of Murcia) and Joaquín Sánchez Soriano (University Miguel Hernández of Elche)
Abstract: This paper deals with the problem of allocating costs in set covering situations. In particular, we focus on set covering situations where the optimal covering is given in advance. Thus, we take into account only the facilities that have to be opened and look for rules distributing their cost. We define a cooperative game and study the core and the nucleolus. We also introduce two new rules: the equal split rule on facilities and the serial rule. We axiomatically characterize the core, the nucleolus, and the two rules. Finally, we study several monotonicity properties of the rules.
Keywords: Set covering problems; Cost sharing rules; Cooperative games.
Jacson Simsen (Universidade Federal de Itajubá), Mariza Stefanello Simsen (Universidade Federal de Itajubá) and José Valero (University Miguel Hernández of Elche).
Abstract: In this work we consider a family of nonautonomous partial differential inclusions governed by p-laplacian operators with variable exponents and large diﬀusion and driven by a forcing nonlinear term of Heaviside type. We prove ﬁrst that this problem generates a sequence of multivalued nonautonomous dynamical systems possessing a pullback attractor. The main result of this paper states that the solutions of the family of partial diﬀerential inclusions converge to the solutions of a limit ordinary diﬀerential inclusion for large diﬀusion and when the exponents go to 2. After that we prove the upper semicontinuity of the pullback attractors.
Keywords: Diﬀerential inclusions; large diﬀusion, reaction-diﬀusion equations; pullback attractors; nonautonomous dynamical systems; multivalued dynamical systems; plaplacian; variable exponent; upper semicontinuity.