José M. Amigó (Miguel Hernández University of Elche) and Yoshito Hirata (The University of Tokyo).
Abstract. The identification of directional couplings (or drive-response relationships) in the analysis of interacting nonlinear systems is an important piece of information to understand their dynamics. This task is especially challenging when the analyst’s knowledge of the systems reduces virtually to time series of observations. Spurred by the success of Granger causality in econometrics, the study of cause-effect relationships (not to be confounded with statistical correlations) was extended to other fields, thus favoring the introduction of further tools such as transfer entropy. Currently, the research on old and new causality tools along with their pitfalls and applications in ever more general situations is going through a time of much activity. In this paper, we re-examine the method of the joint distance distribution to detect directional couplings between two multivariate flows. This method is based on the forced Takens theorem, and, more specifically, it exploits the existence of a continuous mapping from the reconstructed attractor of the response system to the reconstructed attractor of the driving system, an approach that is increasingly drawing the attention of the data analysts. The numerical results with Lorenz and Rössler oscillators in three different interaction networks (including hidden common drivers) are quite satisfactory, except when phase synchronization sets in. They also show that the method of the joint distance distribution outperforms the lowest dimensional transfer entropy in the cases considered. The robustness of the results to the sampling interval, time series length, observational noise, and metric is analyzed too.
Domingo Morales (Miguel Hernández University of Elche), María del Mar Rueda (University of Granada) and Dolores Esteban (Miguel Hernández University of Elche).
Abstract. This paper introduces small area estimators of poverty indexes, with special attention to the poverty rate (or Head Count Index), and studies the sampling design consistency and the asymptotic normality of these estimators. The estimators are assisted by nested error regression models and are model-assisted counterparts of model-based empirical best predictors. Simulation studies show that these estimators present a good balance between sampling bias and mean squared error. Data from the 2013 Spanish living conditions survey with respect to the region of Valencia are used to determine the performance of this new method for estimating the poverty rate.
Jesús T. Pastor (Universidad Miguel Hernández de Elche), Juan Aparicio (Universidad Miguel Hernández de Elche), Javier Alcaraz (Universidad Miguel Hernández de Elche), Fernando Vidal (Universidad Miguel Hernández de Elche) and Diego Pastor (Universidad Miguel Hernández de Elche).
Abstract. Bounded additive models in data envelopment analysis (DEA) under the assumption of constant returns to scale (CRS) were recently introduced in the literature (Cooper et al. in J Product Anal 35(2):85-94, 2011; Pastor et al. in J Product Anal 40:285–292, 2013; Pastor et al. in Omega 56:16–24, 2015). In this paper, we propose to extend the so far generated knowledge about bounded additive models to the family of directional distance function (DDF) models in DEA, giving rise to a completely new subfamily of bounded or partially-bounded CRS-DDF models. We finally check the new approach on a real agricultural panel data set estimating efficiency and productivity change over time, resorting to the Luenberger indicator in a context where at least one variable is naturally bounded.
Václav Kus (Czech Technical University in Prague), Domingo Morales (Universidad Miguel Hernández de Elche), Jitka Hrabáková (Czech Technical University in Prague) and Iva Frýdlová (Czech Technical University in Prague).
Abstract. The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function fo on the real line. It shows that the AMDE always exists when the bounded o-divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, n-1=2 consistency rate in any bounded o-divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family of densities is finite. A simulation experiment empirically studies the performance of the approximate minimum Kolmogorov estimator (AMKE) and some histogram-based variants of approximate minimum divergence estimators, like power type and Le Cam, under six distributions (Uniform, Normal, Logistic, Laplace, Cauchy, Weibull). A comparison with the standard estimators (moment/maximum likelihood/median) is provided for sample sizes n = 10; 20; 50; 120; 250. The simulation analyzes the behaviour of estimators through different families of distributions. It is shown that the performance of AMKE differs from the other estimators with respect to family type and that the AMKE estimators cope more easily with the Cauchy distribution than standard or divergence based estimators, especially for small sample sizes.
Juan Aparicio (University Miguel Hernandez of Elche), Laura López-Torres (University of Alcalá) and Daniel Santín (Complutense University of Madrid).
Abstract. The economic crisis forced politicians to make public finances sustainable. The education sector was one of the most adversely affected by control of public expenditure. This paper analyzes the drivers causing productivity changes of especially vulnerable public schools during the crisis. We use the Hicks-Moorsteen index, which is a seldom applied methodology that leads to feasible results under variable returns to scale. To illustrate the benefits of this index, we use a sample of 298 Catalan public primary schools between 2009 (when budgetary constraints started) and 2014. The results reveal that during the crisis schools improved their total factor productivity by raising academic achievement despite cutbacks in resources. We also found that there was a strong convergence pattern during the financial crisis, driven by the catch-up process of some schools. The findings have important policy implications, suggesting that a monitoring system should be set up for use by policy makers.
Victoria Herranz (Universidad Miguel Hernández), Diego Napp (Universidade de Aveiro Campus Universitário de Santiago) and Carmen Perea (Universidad Miguel Hernández).
Abstract. In this paper we study two different concatenation schemes of twodimensional (2D) convolutional codes. We consider Fornasini–Marchesini state space representation of 2D linear systems to describe our concatenated codes. Also we present upper and lower bounds on the distance of the proposed concatenated codes.