Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  6 Dec 2016 
Place of Publication  Tilburg 
Publisher  
Print ISBNs  9789056684914 
Publication status  Published  2016 
Fingerprint
Cite this
}
Multivariate extreme value statistics for risk assessment. / He, Yi.
Tilburg : CentER, Center for Economic Research, 2016. 142 p.Research output: Thesis › Doctoral Thesis › Scientific
TY  THES
T1  Multivariate extreme value statistics for risk assessment
AU  He, Yi
PY  2016
Y1  2016
N2  This dissertation consists of three essays about statistical estimation and inference methods concerning extremal events and tail risks. The first essay establishes a natural, semiparametric estimation procedure for the multivariate halfspace depthbased extreme quantile region in arbitrary dimensions. In contrast to the failure of fully nonparametric approaches due to the scarcity of extremal observations, the good finitesample performance of our extreme estimator is clearly demonstrated in simulation studies. The second essay extends this method to various depth functions, and, furthermore, establishes an asymptotic approximation theory of whatwecalled (directed) logarithmic distance between our estimated and true quantile region. Confidence sets that asymptotically cover the quantile region or its complement, or both simultaneously, with a prespecified probability can be therefore constructed under weak regular variation conditions. The finitesample coverage probabilities of our asymptotic confidence sets are evaluated in a simulation study for the halfspace depth and the projection depth. We use the procedures in both chapters for risk management by applying them to stock market returns. The third essay develops a statistical inference theory of a recently proposed tail risk measure. For regulators who are interested in monitoring these whatwecalled relative risks of individual banks, we provide a jackknife empirical likelihood inference procedure based on the smoothed nonparametric estimation and a Wilks type of result. A simulation study and reallife data analysis show that the proposed relative risk measure is useful in monitoring systemic risk.
AB  This dissertation consists of three essays about statistical estimation and inference methods concerning extremal events and tail risks. The first essay establishes a natural, semiparametric estimation procedure for the multivariate halfspace depthbased extreme quantile region in arbitrary dimensions. In contrast to the failure of fully nonparametric approaches due to the scarcity of extremal observations, the good finitesample performance of our extreme estimator is clearly demonstrated in simulation studies. The second essay extends this method to various depth functions, and, furthermore, establishes an asymptotic approximation theory of whatwecalled (directed) logarithmic distance between our estimated and true quantile region. Confidence sets that asymptotically cover the quantile region or its complement, or both simultaneously, with a prespecified probability can be therefore constructed under weak regular variation conditions. The finitesample coverage probabilities of our asymptotic confidence sets are evaluated in a simulation study for the halfspace depth and the projection depth. We use the procedures in both chapters for risk management by applying them to stock market returns. The third essay develops a statistical inference theory of a recently proposed tail risk measure. For regulators who are interested in monitoring these whatwecalled relative risks of individual banks, we provide a jackknife empirical likelihood inference procedure based on the smoothed nonparametric estimation and a Wilks type of result. A simulation study and reallife data analysis show that the proposed relative risk measure is useful in monitoring systemic risk.
M3  Doctoral Thesis
SN  9789056684914
T3  CentER Dissertation Series
PB  CentER, Center for Economic Research
CY  Tilburg
ER 