Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)

Cette thèse peut être divisée en trois parties.Dans la première partie, nous étudions des méthodes d'adaptation au niveau de bruit dans le modèle de régression linéaire en grande dimension. Nous prouvons que deux estimateurs à racine carrée, peuvent atteindre les vitesses minimax d'estimation et de prédiction. Nous montrons qu'une version similaire construite à parti de médianes de moyenne, peut encore atteindre les mêmes vitesses optimales en plus d'être robuste vis-à-vis de l'éventuelle présence de données aberrantes.La seconde partie est consacrée à l'analyse de plusieurs modèles de dépendance conditionnelle. Nous proposons plusieurs tests de l'hypothèse simplificatrice qu'une copule conditionnelle est constante vis-à-vis de son évènement conditionnant, et nous prouvons la consistance d'une technique de ré-échantillonage semi-paramétrique. Si la copule conditionnelle n'est pas constante par rapport à sa variable conditionnante, alors elle peut être modélisée via son tau de Kendall conditionnel. Nous étudions donc l'estimation de ce paramètre de dépendance conditionnelle sous 3 approches différentes : les techniques à noyaux, les modèles de type régression et les algorithmes de classification.La dernière partie regroupe deux contributions dans le domaine de l'inférence.Nous comparons et proposons différents estimateurs de fonctionnelles conditionnelles régulières en utilisant des U-statistiques. Finalement, nous étudions la construction et les propriétés théoriques d'intervalles de confiance pour des ratios de moyenne sous différents choix d'hypothèses et de paradigmes. / This thesis can be divided into three parts.In the first part, we study adaptivity to the noise level in the high-dimensional linear regression framework. We prove that two square-root estimators attains the minimax rates of estimation and prediction. We show that a corresponding median-of-means version can still attains the same optimal rates while being robust to outliers in the data.The second part is devoted to the analysis of several conditional dependence models.We propose some tests of the simplifying assumption that a conditional copula is constant with respect to its conditioning event, and prove the consistency of a semiparametric bootstrap scheme.If the conditional copula is not constant with respect to the conditional event, then it can be modelled using the corresponding Kendall's tau.We study the estimation of this conditional dependence parameter using 3 different approaches : kernel techniques, regression-type models and classification algorithms.The last part regroups two different topics in inference.We review and propose estimators for regular conditional functionals using U-statistics.Finally, we study the construction and the theoretical properties of confidence intervals for ratios of means under different sets of assumptions and paradigms.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18620号 / 情博第544号 / 新制||情||96(附属図書館) / 31520 / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 多々納 裕一, 教授 矢守 克也, 教授 堀 智晴 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Risk assessment for natural hazards and financial extreme events requires the statistical analysis of extreme events, often beyond observed levels. The characterization and extrapolation of the probability of rare events rely on assumptions about the extremal dependence type and about the specific structure of statistical models. In this thesis, we develop models with flexible tail dependence structures, in order to provide a reliable estimation of tail characteristics and risk measures. From a methodological perspective, this thesis makes the following novel developments. 1) We propose new copula-based models for multivariate and spatial extremes with flexible tail dependence structures, which are parsimonious and able to bridge smoothly asymptotic dependence and asymptotic independence classes, in both the upper and the lower tails; 2) Moreover, aiming at describing more general dependence structures using graphs, we propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC) under the framework of regular variation to learn complex extremal network structures; 3) Finally, we develop a semi-parametric neural-network-based regression model to identify spatial causal effects at all quantile levels (including low and high quantiles). Overall, we make novel contributions to creating new flexible extremal dependence models, developing and implementing novel Bayesian computation algorithms, and taking advantage of machine learning and causal inference principles for modeling extremes. Our novel methodologies are illustrated by a range of applications to financial, climatic, and health data. Specifically, we apply our bivariate copula model to the historical closing prices of five leading cryptocurrencies and estimate the extremal dependence evolution over time, and we use the PTCC to learn the extreme risk network of historical global currency exchange data. Moreover, our multivariate spatial factor copula model is applied to study the upper and lower extremal dependence structures of the daily maximum and minimum air temperature from the state of Alabama in the southeastern United States; and we also apply the PTCC in extreme river discharge network learning for the Upper Danube basin. Finally, we apply the causal spatial quantile regression model in quantifying spatial quantile treatment effects of maternal smoking on extreme low birth weight of newborns in North Carolina, United States.

Recognizing the distinct non-motorist injury severity profiles by crash location (segment or intersection), we propose a joint modeling framework to study crash location type and non-motorist injury severity as two dimensions of the severity process. We employ a copula-based joint framework that ties the crash location type (represented as a binary logit model) and injury severity (represented as a generalized ordered logit model) through a closed form flexible dependency structure to study the injury severity process. The data for our analysis is drawn from the Central Florida region for the years of 2015 to 2021. The model system explicitly accounts for temporal heterogeneity across the two dimensions. A comprehensive set of independent variables including non-motorist user characteristics, driver and vehicle characteristics, roadway attributes, weather and environmental factors, temporal and sociodemographic factors are considered for the analysis. We also conducted an elasticity analysis to show the actual magnitude of the independent variables on non-motorist injury severity at the two locations. The results highlight the importance of examining the effect of various independent variables on non-motorist injury severity outcome by different crash locations.

In this thesis, we suggest a goodness-ofit test for semi-parametric copula models. We extended the pseudo in-and-out-sample (PIOS) test proposed in [17], which is based on the PIOS test in [28]. The PIOS test is constructed by comparing the pseudo "in-sample" likelihood and pseudo "out-of-sample" likelihood. Our contribution is twoold. First, we use the approximate test statistics instead of the exact test statistics to alleviate the computational burden of calculating the test statistics. Secondly, we propose a parametric bootstrap procedure to approximate the distribution of the test statistic. Unlike the nonparametric bootstrap which resamples from the original data, the parametric procedure resamples the data from the copula model under the null hypothesis. We conduct simulation studies to investigate the performance of the approximate test statistic and parametric bootstrap. The results show that the parametric bootstrap presents higher test power with a well-controlled type I error compared to the nonparametric bootstrap.

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An asset manager's goal is to provide a high return relative the risk taken, and thus faces the challenge of how to choose an optimal portfolio. Many mathematical methods have been developed to achieve a good balance between these attributes and using di erent risk measures. In thisthesis, we test the use of a relatively simple and common approach: the Markowitz mean-variance method, and a more quantitatively demanding approach: the tail optimization method. Using active portfolio based on data provided by the Swedish fund management company Enter Fonderwe implement these approaches and compare the results. We analyze how each method weighs theunderlying assets in order to get an optimal portfolio.