Extreme Risk Measures
Expectile Based Tail Index Estimation
High Expectile Estimation
Extreme Level Estimation
Multidimensional High Expectile Estimation
Expectile Computation
Marginal Expected Shortfall Expectile Based Estimation
Multidimensional Value-at-Risk (VaR) or Extreme Quantile (EQ) Estimati...
Value-at-Risk (VaR) or Extreme Quantile (EQ) Estimation
Hill Tail Index Estimation
Wald-Type Hypothesis Testing
Maximum Likelihood Tail Index Estimation
Moment based Tail Index Estimation
Multidimensional Hill Tail Index Estimation
Extreme Expectile Estimation
Multidimensional Extreme Expectile Estimation
Marginal Expected Shortfall Quantile Based Estimation
Simulation of Two-Dimensional Temporally Dependent Observations
Simulation of -Dimensional Temporally Independent Observations
Simulation of One-Dimensional Temporally Dependent Observations
A set of procedures for estimating risks related to extreme events via risk measures such as Expectile, Value-at-Risk, etc. is provided. Estimation methods for univariate independent observations and temporal dependent observations are available. The methodology is extended to the case of independent multidimensional observations. The statistical inference is performed through parametric and non-parametric estimators. Inferential procedures such as confidence intervals, confidence regions and hypothesis testing are obtained by exploiting the asymptotic theory. Adapts the methodologies derived in Padoan and Stupfler (2020) <arxiv:2004.04078>, Padoan and Stupfler (2020) <arxiv:2007.08944>, Daouia et al. (2018) <doi:10.1111/rssb.12254>, Drees (2000) <doi:10.1214/aoap/1019487617>, Drees (2003) <doi:10.3150/bj/1066223272>, de Haan and Ferreira (2006) <doi:10.1007/0-387-34471-3>, de Haan et al. (2016) <doi:10.1007/s00780-015-0287-6>.