Learning Theory and Approximation

The main goal of this workshop – the third one of this type at the MFO – has been to blend mathematical results from statistical learning theory and approximation theory to strengthen both disciplines and use synergistic effects to work on current research questions. Learning theory aims at modeling unknown function relations and data structures from samples in an automatic manner. Approximation theory is naturally used for the advancement and closely connected to the further development of learning theory, in particular for the exploration of new useful algorithms, and for the theoretical understanding of existing methods. Conversely, the study of learning theory also gives rise to interesting theoretical problems for approximation theory such as the approximation and sparse representation of functions or the construction of rich kernel reproducing Hilbert spaces on general metric spaces. This workshop has concentrated on the following recent topics: Pitchfork bifurcation of dynamical systems arising from mathematical foundations of cell development; regularized kernel based learning in the Big Data situation; deep learning; convergence rates of learning and online learning algorithms; numerical refinement algorithms to learning; statistical robustness of regularized kernel based learning

Estimating Dependences and Risk between Gold Prices and S&P500: New Evidences from ARCH,GARCH, Copula and ES-VaR models

This thesis examines the correlations and linkages between the stock and commodity in order to quantify the risk present for investors in financial market (stock and commodity) using the Value at Risk measure. The risk assessed in this thesis is losses on investments in stock (S&P500) and commodity (gold prices). The structure of this thesis is based on three empirical chapters. We emphasise the focus by acknowledging the risk factor which is the non-stop fluctuation in the prices of commodity and stock prices. The thesis starts by measuring volatility, then dependence which is the correlation and lastly measure the expected shortfalls and Value at risk (VaR). The research focuses on mitigating the risk using VaR measures and assessing the use of the volatility measures such as ARCH and GARCH and basic VaR calculations, we also measured the correlation using the Copula method. Since, the measures of volatility methods have limitations that they can measure single security at a time, the second empirical chapter measures the interdependence of stock and commodity (S&P500 and Gold Price Index) by investigating the risk transmission involved in investing in any of them and whether the ups and downs in the prices of one effect the prices of the other using the Time Varying copula method. Lastly, the third empirical chapter which is the last chapter, investigates the expected shortfalls and Value at Risk (VaR) between the S&P500 and Gold prices Index using the ES-VaR method proposed by Patton, Ziegel and Chen (2018). Volatility is considered to be the most popular and traditional measure of risk. For which we have used ARCH and GARCH model in our first empirical chapter. However, the problem with volatility is that it does not take into account the direction of an investments’ movement: volatility of stocks is that they suddenly jump higher and investors are not distressed with gains. When we talk about investors for them the risk is about the odds of losing money, after my research and findings VaR is based on the common-sense fact. Hence, investors care about the odds of big losses, VaR answers the question, what is my worst-case scenario? Or simply how much I could lose in a really bad month? The results of the thesis demonstrated that measuring volatility (ARCH GARCH) alone was not sufficient in measuring the risk involved in an investment therefore methodologies such as correlation and VAR demonstrates better results. In terms of measuring the interdependence, the Time Varying Copula is used since the dynamic structure of the de- pendence between the data can be modelled by allowing either the copula function or the dependence parameter to be time varying. Lastly, hybrid model further demonstrates the average return on a risky asset for which Expected Shortfall (ES) along with some quantile dependence and VaR (Value at risk) is utilised. Basel III Accord which is applied in coming years till 2019 focuses more on ES unlike VaR, hence there is little existing work on modelling ES. The thesis focused on the results from the model of Patton, Ziegel and Chen (2018) which is based on the statistical decision theory. Patton, Ziegel and Chen (2018), overcame the problem of elicitability for ES by using ES and VaR jointly and propose the new dynamic model of risk measure. This research adds to the contribution of knowledge that measuring risk by using volatility is not enough for measuring risk, interdependence helps in measuring the dependency of one variable over the other and estimations and inference methods proposed by Patton, Ziegel and Chen (2018) using simulations proposed in ES-VaR model further concludes that ARCH and GARCH or other rolling window models are not enough for determining the risk forecasts. The results suggest, in first empirical chapter we see volatility between Gold prices and S&P500. The second empirical chapter results suggest conditional dependence of the two indexes is strongly time varying. The correlation between the stock is high before 2008. The results further displayed slight stronger bivariate upper tail, which signifies that the conditional dependence of the indexes is influence by positive shocks. The last empirical chapter findings proposed that measuring forecasts using ES-Var model proposed by Patton, Ziegel and Chen (2018) does outer perform forecasts based on univariate GARCH model. Investors want to 10 protect themselves from high losses and ES-VaR model discussed in last chapter would certainly help them to manage their funds properly

Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference

Peer ReviewedPostprint (published version

Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference

Artículos presentados en la International Conference on Risk Analysis ICRA 6/RISK 2015, celebrada en Barcelona del 26 al 29 de mayo de 2015.Peer ReviewedPostprint (published version

Composing the cumulative quantile regression function and the Goldie concentration curve

The model we discuss in this paper deals with inequality in distribution in the presence of a covariate. To elucidate that dependence, we propose to consider the composition of the cumulative quantile regression (CQR) function and the Goldie concentration curve, the standardized counterpart of which gives a fraction to fraction plot of the response and the covariate. It has the merit of enhancing the visibility of inequality in distribution when the latter is present. We shall examine the asymptotic properties of the corresponding empirical estimator. The associated empirical process involves a randomly stopped partial sum process of induced order statistics. Strong Gaussian approximations of the processes are constructed. The result forms the basis for the asymptotic theory of functional statistics based on these processes.Goldie concentration curve Cumulative quantile regression function Induced order statistics Lorenz curve Strong Gaussian approximations

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Temas de actualidad en salud pública

La salud pública es una disciplina importante para la salud en el mundo. Se define como la ciencia y el arte de prevenir las enfermedades, prolongar la vida y promover la salud a través de los esfuerzos organizados y decisiones con conocimiento de la sociedad, las organizaciones (públicas y privadas), las comunidades y los individuos, esta disciplina se ha renovado con la incorporación de múltiples actores, profesiones, áreas de conocimiento, además de ser afectados y promovido por múltiples tecnologías, en particular los de información. Como un campo cambiante del conocimiento, la salud pública requiere la información basada en la evidencia y actualizaciones regulares, más aún en el contexto de un mundo en transición epidemiológica. "Temas actuales en la salud pública", presenta información actualizada sobre varios temas relacionados con las áreas reales de interés en esta ciencia médica creciente y emocionante, con la concepción y la filosofía que estamos trabajando para mejorar la salud de la población, en lugar que el tratamiento de las enfermedades de los pacientes individuales, la toma de decisiones sobre el cuidado de la salud colectiva que se basan en la mejor evidencia disponible, actualizada, válida y pertinente, y, finalmente, en el contexto de los recursos disponibles. La salud pública debe ser una ciencia compleja, ayudando en las decisiones, acciones y cambios en la salud del mundo. En una sociedad globalizada esto se hizo hincapié no sólo en una nación en particular, sino en todo el mundo.Public health is a major health discipline in the world. Defined as the science and art of preventing diseases, prolonging life and promoting health through the organized efforts and informed choices of the society, organizations (public and private), communities and individuals, this discipline has been renewed by the incorporation of multiple actors, professions, knowledge areas, as well as being impacted and promoted by multiple technologies, particularly information ones. As a changing field of knowledge, public health requires evidence-based information and regular updates, even more in the context of a world in epidemiological transition. Health impacts of climate change are currently in the quest of the Millennium Development Goals, and most of them are related to the activities of public health. “Current Topics in Public Health” presents updated information on multiple topics related to actual areas of interest in this growing and exciting medical science, with the conception and philosophy that we are working to improve the health of the population, rather than treating diseases of individual patients; taking decisions about collective health care that are based on the best available, current, valid and relevant evidence; and finally within the context of available resources. Public health should be a complex science helping in the decision, actions and changes in the health of the world. In a globalized society this is emphasized not just in a particular nation but in the whole world

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement