Correction to: Estimation and uncertainty quantification for extreme quantile regions

1 Section 2.2

• Page 6, line 26: Equation (2.9) should be

  $$ \begin{array}{@{}rcl@{}} t\left( 1-F(tU_{1}(x_{1}), tU_{2}(x_{2}))\right) \overset{t \to \infty}{\longrightarrow} -\log G_{*}(\boldsymbol{x}). \end{array} $$

• Page 7, line 5: Equation (2.10) should be

  $$ \begin{array}{@{}rcl@{}} tU_{1}(t)U_{2}(t)f\left( tU_{1}(x_{1}), tU_{2}(x_{2})\right) \overset{t \to \infty}{\longrightarrow} (\gamma_{1}\gamma_{2})^{-1}x_{1}^{1-\gamma_{1}}x_{2}^{1-\gamma_{2}}g(\boldsymbol{x}) =: q(\boldsymbol{x}). \end{array} $$

2 Section 3.1

• Page 8, line 10 & 11: “The threshold may then be defined as T = X_n−k,n for large k such that 1 − F_n(X_n−k,n) = k/n is close to zero, for instance k/n = 0.10,0.05,0.01.”

• Page 8, line 21: The derivative should be with respect to y, i.e. $\frac {\partial }{\partial y} G^{k/n}(y;\boldsymbol {\theta })|_{y=y_{i}}$

3 Section 3.2

• Page 12, Algorithm 1: The acceptance rules should be π₁ > U₁, π₂ > U₂ and π₃ > U₃.