[00539] Extreme value theory and statistical analysis
Session Time & Room : 4D (Aug.24, 15:30-17:10) @F412
Type : Proposal of Minisymposium
Abstract : Huge disasters, such as earthquake and flood occur rarely but their damage is extremely terrible and the countermeasures against them are urgent social task.
Extreme value theory (EVT) deals with rare events mathematically or statistically and is applied to risk management for not only disasters but also various fields, for example, finance, insurance and life span of industrial products.
We present 4 researches. Asymptotic theory for extreme value generalized additive model, statistical inference for sample maximum distribution, nonparametric statistical inference related to several economic topics and statistical management for multivariate risk for financial institutions.
[03480] Asymptotic theory for extreme value generalized additive model
Format : Talk at Waseda University
Author(s) :
Takuma Yoshida (Kagoshima University)
Abstract : The classical approach to analyzing extreme value data is the generalized Pareto distribution
(GPD). When the GPD is used to explain a target variable with the large dimension
of covariates, the shape and scale function of covariates included in GPD are sometimes
modeled using the generalized additive models (GAM). In contrast to many results of application,
there are no theoretical results on the hybrid technique of GAM and GPD, which
motivates us to develop its asymptotic theory. We provide the rate of convergence of the
estimator of shape and scale functions, as well as its local asymptotic normality.
[03597] Comparative study on accuracy of sample maximum distribution estimators in IID settings
Format : Online Talk on Zoom
Author(s) :
Taku Moriyama (Yokohama City University)
Abstract : Comparative study on the accuracy of sample maximum distribution estimators in IID settings will be reported. The distribution of sample maximum is approximated by the generalized extreme value distribution. However, the approximation accuracy heavily depends on the tail index. This study investigates a nonparametric estimator as the alternative approach and compares the accuracies both theoretically and numerically. Future prospects of the study will also be discussed.
[02777] Subsampling inference for nonparametric extremal conditional quantiles
Format : Talk at Waseda University
Author(s) :
Daisuke Kurisu (The University of Tokyo)
Taisuke Otsu (London School of Economics)
Abstract : In this talk, we study asymptotic properties of the local linear (LL) quantile estimator under the extremal-order quantile asymptotics and develop a practical inference method for conditional quantiles in extreme tail areas. The asymptotic distribution of the LL quantile estimator is derived as a minimizer of certain functional of a Poisson point process. We also propose a subsampling inference method for conditional extreme quantiles based on a self-normalized version of the LL estimator.
[03093] Measuring non-exchangeable tail dependence using tail copulas
Format : Talk at Waseda University
Author(s) :
Takaaki Koike (Hitotsubashi University)
Shogo Kato (Institute of Statistical Mathematics)
Marius Hofert (The University of Hong Kong)
Abstract : We propose a novel framework of quantifying and comparing the degree of tail dependence using tail copula. Our proposed measures have clear probabilistic interpretations, and capture various features of non-exchangeable tail dependence depending on the purpose of the analysis. Analytical forms of the proposed measures are derived for various parametric copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.
