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Los órdenes estocásticos o las dominancias estocásticas tal como se conocen en Economía se han estudiado y aplicado ampliamente en diversidad de campos científicos, desde la Biología hasta la Ingeniería de Sistemas. Sin embargo, hasta donde llega nuestro conocimiento hay una laguna de aplicación dentro del ámbito de las Ciencias del Deporte. En este trabajo, pretendemos una primera aproximación a una posible aplicación de los órdenes estocásticos a un conjunto de datos de partidos de fútbol de LaLiga (España). Nuestro objetivo simplemente es mostrar como se puede ampliar una comparativa más allá de una simple comparación de métricas globales o totales. En particular, nos detendremos en los órdenes de dominancia estocástica de primer y segundo orden por ser los más intuitivos y de más sencilla interpretación y por ser los más usados en Economía., Stochastic orders or stochastic dominance as they are known in economics, have been widely studied and applied in a variety of scientific fields, from biology to Systems Engineering. However, to the best of our knowledge, there is an application gap in the field of Sports Analytics or Sports Sciences. In this paper, we attempt a first approach to a possible application of stochastic orders to a dataset of LaLiga (Spain) football matches. Our aim is simply to show how a comparison can be extended beyond a simple metric comparison. In particular, we will focus on the first and second dominance stochastic orders as they are the most intuitive and simple to interpret and are also the most widely used in economics.

The dissemination of research in cultural heritage preservation to the public is a task that needs new models and expressions, to capture the attention of the public and the assessment of results. With this purpose, a new educa‑ tional experience in Parque de las Ciencias (Science Park of Granada, Spain) was developed. The science window titled Hidden Face of Cultural Heritage (ScW‑CH) was an exhibition to show the risks (hazards + vulnerability) associ‑ ated to different artworks and materials of our cultural heritage (CH). ScW‑CH was led by the researchers themselves, in collaboration with museum specialists, in order to develop a new model that makes their research accessible to all demographics. An innovative methodology based into simulating a showcase, was designed to study hazards and vulnerability in CH. Therefore, the montage contained materials, equipment, information sheets, and guides to accompany visitors as storytellers. The aim of the exhibition, was for the visitors to understand the risks posed to our monuments and artworks from a scientific point of view, and to raise awareness about the care that we should give to our CH. The ScW‑CH was held for 6 months and visited by 8226 visitors. During the exhibition, a survey about the opinion of visitors was carried out to study the impact of the designed new model and assess the results of the expe‑ rience. The collected data was analysed by the Statistical Package for the Social Sciences (version 22.0). Visitors usually presented a medium–high initial interest about visiting this exhibition, and a medium–low level of knowledge of this subject. Thanks to ScW‑CH, 92% of visitors showed a very high learning level after the experience. The ratio of interest and learning in the ScW‑CH in relationship with the level of study showed that secondary school pupils had the high‑ est degree of interest and learning.

Como consecuencia de que los reguladores necesitan gestionar el riesgo en los distintos sectores, se está extendiendo de forma rápida una metodología basada en el riesgo. En las últimas décadas, este problema ha sido tratado en su mayoría en una versión univariante. Sin embargo, los riesgos envuelven normalmente varias variables aleatorias que son a menudo dependientes. Por tanto, es crucial trabajar en un marco multivariante. Por otro lado, los fenómenos están caracterizados frecuentemente por eventos extremos. Esta tesis trata fundamentalmente dos problemas: la definición de medidas de riesgo en un marco multivariante y la estimatión de medidas de riesgo multivariantes teniendo en cuenta eventos extremos. El Capítulo 1 es un capítulo introductorio. Presentamos el estado del arte para la noción de medidas de riesgo multivariantes. También, recordamos los principales resultados en Teoría de Cópulas, Teoría de Valores Extremos y Órdenes Estocásticos que son útiles en este trabajo . Se introducen dos nuevas medidas de riesgo multivariantes en el Capítulo 2. Varias propiedades interesantes y, caracterizaciones bajo condiciones de cópulas Arquimedianas, se estudian para las medidas de riesgo propuestas. Además, se obtienen estimadores semiparamétricos para las nuevas medidas, y son ejempli_cados considerando datos simulados y un conjunto de datos real de seguros. El Capítulo 3 se centra en la estimación extrema no paramétrica de las medidas multivariantes propuestas en el Capítulo 2. Para este propósito, primero analizamos el comportamiento en la cola de las distribuciones condicionadas que de_nen dichas medidas. El principal resultado está constituido por el Teorema Central del Límite de los estimadores extremos. El rendimiento de los estimadores extremos se evalúa en datos simulados y para un conjunto de datos real de precipitaciones. El estudio de la medida de riesgo multivariante asociada con the Component-wise Excess(C.-E.) design realization dada por Salvadori et, As a consequence of the need for regulators to manage risk in various sectors, a riskbased methodology is undergoing a fast expansion. Over recent decades, this problem has been mostly addressed via a univariate approach. However, risks usually involve several random variables that are often non-independent. Therefore, it is crucial to work in a multivariate setting. On the other hand, phenomena are frequently characterized by extreme events. This thesis is fundamentally concerned with two problems: the de_nition of risk measures in a multivariate setting, and the estimation of multivariate risk measures by taking extreme events into account. Chapter 1 is an introductory chapter. We present the state-of-art of the notion of multivariate risk measures. The main results in Copula Theory, Extreme Value Theory, and Stochastic Orders, which are useful in this work, are also provided. Two new multivariate risk measures are introduced in Chapter 2. Several interesting properties and, characterizations under Archimedean copulas, are studied for the proposed risk measures. Furthermore, semi-parametric estimators for the new measures are obtained and are then exempli_ed considering simulated data and a real insurance data-set. Chapter 3 deals with the non-parametric extreme estimation procedure of the multivariate measures proposed in Chapter 2. For this purpose, we _rst analyse the tail behaviour of the conditional distributions that de_ne the aforementioned measures. The main result is given by the Central limit Theorem of the extreme estimators. The performance of the extreme estimators is evaluated in simulated data and for a real rainfall data-set. The multivariate risk measure associated with the Component-wise Excess (C.-E.) design realization given by Salvadori et al. (2011) is outlined in Chapter 4. The explicit expression of the measure for Archimedean copulas is obtained. In addition, an extreme estimation procedure for the C.-E. design realization is provided and

CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2011) able to measure a financial institution’s contribution to systemic risk and its contribution to the risk of other financial institutions. CoVaR stands for conditional Value-at-Risk, i.e. it indicates the Value at Risk for a financial institution that is conditional on a certain scenario. In this paper, two alternative extensions of the classic univariate Conditional Value-at-Risk are introduced in a multivariate setting. The two proposed multivariate CoVaRs are constructed from level sets of multivariate distribution functions (resp. of multivariate survival distribution functions). These vector-valued measures have the same dimension as the underlying risk portfolio. Several characterizations of these new risk measures are provided in terms of the copula structure and stochastic orderings of the marginal distributions. Interestingly, these results are consistent with existing properties on univariate risk measures. Furthermore, comparisons between existent risk measures and the proposed multivariate CoVaR are developed. Illustrations are given in the class of Archimedean copulas. Estimation procedure for the multivariate proposed CoVaRs is illustrated in simulated studies and insurance real data.

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article.

Multivariate lifetime data frequently arise so it is important to consider different multivariate distributions that could be used to model aging concepts. The generalization of univariate versions has two main problems. One of them is the concept of the multivariate quantile and the other one is that the survival function valued at a multivariate quantile depends on the underlying distributions. For this reason, a new multivariate aging concept based on the upper corrected orthant is developed. This new multivariate aging is a generalization of the New Better than Used in Expectation univariate version and a characterization by using the multivariate excess wealth function is provided. Finally, data from the Comprehensive Cohort Study performed by the German Breast Cancer Study Group are analysed in order to estimate the parameters in a non-deterministic model which describes the tumor growth and to realize how this new multivariate ageing notion influences in the final results.

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate rightspread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are described.

Las distribuciones de visa son de gran importancia en la teoría de modelización estocástica, teoría de la renovación, fiabilidad y análisis de supervivencia. El envejecimiento de un sistema físico o biológico se conoce como el fenóm ... eno por el cual un sistema más antiguo tiene un menor tiempo de vida, en algún sentido estocástico, que un sistema más nuevo. Muchos de los criterios de envejecimiento (por ejemplo, las nociones IFR, DMRL y NBUE) se han desarrollado en la literatura durante muchos años y han sido también propuestas y estudiadas. Cabe mencionar que muchos de estos métodos se incluyen en el marco del ordenamiento estocástico.Esta Tesis Doctoral está centrada fundamentalmente en dos objetivos: Estudiar nuevas nociones de envejecimiento multivariante y caracterizar dichas nociones por medio de una función de dispersión multivariante, generalizando así los resultados ya estudiados en el caso univariante por Fernández-once et al. (1996) and Fernández-Ponce et al. (1998). Para el estudio de estos objetivos, dos conceptos fundamentales son tomados como punto de partida, también conocido como construcción estándar, fue definido por primera vez por O´brien (1975), y ha sido ampliamente utilizado en teoría de simulación así como en la teoría de ordenaciones estocásticas. El segundo concepto fue dado por Fernández-Ponce y el Suárez-Lloréns (2003). Estos autores proporcionaron el concepto de cuadrante superior corregido asociado con la construcción estándar y obtuvieron el importante resultado de que la probabilidad acumulada en esta región no depende de la distribución considerada. Estos conceptos, junto con el trabajo de Fernández-Ponce et al. (1998), donde las nociones de envejecimiento univariante son caracterizan por la función de exceso de riqueza (excess-wealth), es la base para el desarrollo de esta investigación. Obviamente, numerosos resultados significativos en fiabilidad y en el área de ordenaciones estocásticas son considerados con el fin de alcanzar